M. J. Ablowitz, B. Prinari, and A. D. Trubatch, “Integrable nonlinear Schrödinger systems and their soliton dynamics,” Dyn. Partial Differ. Equ. 1, 239–299 (2004).

N. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “The inverse scattering transform-Fourier analysis for nonlinear problems,” Stud. Appl. Math. 53, 249–315 (1974).

[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2013).

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

C. Xie, M. Karlsson, P. A. Andrekson, H. Sunnerud, and J. Li, “Influences of polarization-mode dispersion on soliton transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 575–590 (2002).

[Crossref]

S. T. Le, V. Aref, and H. Buelow, “Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 11, 570–576 (2017).

[Crossref]

V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental demonstration of nonlinear frequency division multiplexed transmission,” in 41st European Conference on Optical Communications (ECOC) (2015), paper Tu.1.1.2.

V. Aref, S. T. Le, and H. Buelow, “Demonstration of fully nonlinear spectrum modulated system in the highly nonlinear optical transmission regime,” in 42st European Conference on Optical Communications (ECOC) (2016), paper Th.3.B.2.

V. Aref, “Control and detection of discrete spectral amplitudes in nonlinear Fourier spectrum,” arXiv:1605.06328 (2016).

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett. 113, 013901 (2014).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

S. T. Le, V. Aref, and H. Buelow, “Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 11, 570–576 (2017).

[Crossref]

V. Aref, S. T. Le, and H. Buelow, “Demonstration of fully nonlinear spectrum modulated system in the highly nonlinear optical transmission regime,” in 42st European Conference on Optical Communications (ECOC) (2016), paper Th.3.B.2.

T. Gui, T. H. Chan, C. Lu, A. P. T. Lau, and P. K. A. Wai, “Alternative decoding methods for optical communications based on nonlinear Fourier transform,” J. Lightwave Technol. 35, 1542–1550 (2017).

[Crossref]

Q. Zhang and T. H. Chan, “A Gaussian noise model of spectral amplitudes in soliton communication systems,” in IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (IEEE, 2015), pp. 455–459.

Q. Zhang and T. H. Chan, “A spectral domain noise model for optical fibre channels,” in IEEE International Symposium on Information Theory, June2015, pp. 1660–1664.

Q. Zhang and T. H. Chan, “Noise models in the nonlinear spectral domain for optical fibre communications,” arXiv:1702.06226 (2017).

Y. Chen and H. Haus, “Manakov solitons and polarization mode dispersion,” Chaos 10, 529–538 (2000).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[Crossref]

S. Gaiarin, A. M. Perego, E. Porto da Silva, F. Da Ros, and D. Zibar, “Experimental demonstration of dual polarization nonlinear frequency division multiplexed optical transmission system,” in 43rd European Conference on Optical Communications (ECOC) (2017), paper W.3.C.2.

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[Crossref]

S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4, 307–322 (2017).

[Crossref]

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett. 113, 013901 (2014).

[Crossref]

S. A. Derevyanko, J. E. Prilepsky, and D. A. Yakushev, “Statistics of a noise-driven Manakov soliton,” J. Phys. A 39, 1297–1309 (2006).

[Crossref]

R. G. Docksey and J. N. Elgin, “Closure of the Manakov system,” SIAM J. Math. Anal. 32, 54–79 (2000).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

T. P. Horikis and J. N. Elgin, “Nonlinear optics in a birefringent optical fiber,” Phys. Rev. E 69, 016603 (2004).

[Crossref]

R. G. Docksey and J. N. Elgin, “Closure of the Manakov system,” SIAM J. Math. Anal. 32, 54–79 (2000).

[Crossref]

S. T. Le, I. D. Phillips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightwave Technol. 34, 2459–2466 (2016).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett. 113, 013901 (2014).

[Crossref]

S. Gaiarin, A. M. Perego, E. Porto da Silva, F. Da Ros, and D. Zibar, “Experimental demonstration of dual polarization nonlinear frequency division multiplexed optical transmission system,” in 43rd European Conference on Optical Communications (ECOC) (2017), paper W.3.C.2.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

N. Nabavi and T. J. Hall, “Demultiplexing by independent component analysis in coherent optical transmission: the polarization channel alignment problem,” in Photonics North (2015).

S. T. Le, I. D. Phillips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightwave Technol. 34, 2459–2466 (2016).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

Y. Chen and H. Haus, “Manakov solitons and polarization mode dispersion,” Chaos 10, 529–538 (2000).

[Crossref]

T. P. Horikis and J. N. Elgin, “Nonlinear optics in a birefringent optical fiber,” Phys. Rev. E 69, 016603 (2004).

[Crossref]

V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental demonstration of nonlinear frequency division multiplexed transmission,” in 41st European Conference on Optical Communications (ECOC) (2015), paper Tu.1.1.2.

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4, 307–322 (2017).

[Crossref]

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “On the design of NFT-based communication systems with lumped amplification,” J. Lightwave Technol. 35, 5464–5472 (2017).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

C. Xie, M. Karlsson, P. A. Andrekson, H. Sunnerud, and J. Li, “Influences of polarization-mode dispersion on soliton transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 575–590 (2002).

[Crossref]

T. Lakoba and D. Kaup, “Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers,” Phys. Rev. E 56, 6147–6165 (1997).

[Crossref]

N. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “The inverse scattering transform-Fourier analysis for nonlinear problems,” Stud. Appl. Math. 53, 249–315 (1974).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

S. Hari, M. I. Yousefi, and F. R. Kschischang, “Multieigenvalue communication,” J. Lightwave Technol. 34, 3110–3117 (2016).

[Crossref]

S. Hari and F. R. Kschischang, “Bi-directional algorithm for computing discrete spectral amplitudes in the NFT,” J. Lightwave Technol. 34, 3529–3537 (2016).

[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part I: mathematical tools,” IEEE Trans. Inf. Theory 60, 4312–4328 (2014).

[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part III: spectrum modulation,” IEEE Trans. Inf. Theory 60, 4346–4369 (2014).

[Crossref]

T. Lakoba and D. Kaup, “Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers,” Phys. Rev. E 56, 6147–6165 (1997).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4, 307–322 (2017).

[Crossref]

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “On the design of NFT-based communication systems with lumped amplification,” J. Lightwave Technol. 35, 5464–5472 (2017).

[Crossref]

S. T. Le, V. Aref, and H. Buelow, “Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 11, 570–576 (2017).

[Crossref]

S. T. Le, I. D. Phillips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightwave Technol. 34, 2459–2466 (2016).

[Crossref]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express 23, 8317–8328 (2015).

[Crossref]

V. Aref, S. T. Le, and H. Buelow, “Demonstration of fully nonlinear spectrum modulated system in the highly nonlinear optical transmission regime,” in 42st European Conference on Optical Communications (ECOC) (2016), paper Th.3.B.2.

C. Xie, M. Karlsson, P. A. Andrekson, H. Sunnerud, and J. Li, “Influences of polarization-mode dispersion on soliton transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 575–590 (2002).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

A. Maruta and Y. Matsuda, “Polarization division multiplexed optical eigenvalue modulation,” in International Conference on Photonics in Switching (PS), Florence, Italy (2015), pp. 265–267.

A. Maruta and Y. Matsuda, “Polarization division multiplexed optical eigenvalue modulation,” in International Conference on Photonics in Switching (PS), Florence, Italy (2015), pp. 265–267.

V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer-Verlag, 1991).

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fiber communications,” Nature 411, 1027–1030 (2001).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

N. Nabavi and T. J. Hall, “Demultiplexing by independent component analysis in coherent optical transmission: the polarization channel alignment problem,” in Photonics North (2015).

N. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “The inverse scattering transform-Fourier analysis for nonlinear problems,” Stud. Appl. Math. 53, 249–315 (1974).

[Crossref]

A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightwave Technol. 11, 395–399 (1993).

[Crossref]

S. Gaiarin, A. M. Perego, E. Porto da Silva, F. Da Ros, and D. Zibar, “Experimental demonstration of dual polarization nonlinear frequency division multiplexed optical transmission system,” in 43rd European Conference on Optical Communications (ECOC) (2017), paper W.3.C.2.

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

S. T. Le, I. D. Phillips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightwave Technol. 34, 2459–2466 (2016).

[Crossref]

S. Gaiarin, A. M. Perego, E. Porto da Silva, F. Da Ros, and D. Zibar, “Experimental demonstration of dual polarization nonlinear frequency division multiplexed optical transmission system,” in 43rd European Conference on Optical Communications (ECOC) (2017), paper W.3.C.2.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4, 307–322 (2017).

[Crossref]

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “On the design of NFT-based communication systems with lumped amplification,” J. Lightwave Technol. 35, 5464–5472 (2017).

[Crossref]

S. T. Le, I. D. Phillips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightwave Technol. 34, 2459–2466 (2016).

[Crossref]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express 23, 8317–8328 (2015).

[Crossref]

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett. 113, 013901 (2014).

[Crossref]

S. A. Derevyanko, J. E. Prilepsky, and D. A. Yakushev, “Statistics of a noise-driven Manakov soliton,” J. Phys. A 39, 1297–1309 (2006).

[Crossref]

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, “Integrable nonlinear Schrödinger systems and their soliton dynamics,” Dyn. Partial Differ. Equ. 1, 239–299 (2004).

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer-Verlag, 1991).

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental demonstration of nonlinear frequency division multiplexed transmission,” in 41st European Conference on Optical Communications (ECOC) (2015), paper Tu.1.1.2.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

N. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “The inverse scattering transform-Fourier analysis for nonlinear problems,” Stud. Appl. Math. 53, 249–315 (1974).

[Crossref]

V. E. Zakharov and A. B. Shabat, “Exact theory of 2-dimensional self- focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fiber communications,” Nature 411, 1027–1030 (2001).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

C. Xie, M. Karlsson, P. A. Andrekson, H. Sunnerud, and J. Li, “Influences of polarization-mode dispersion on soliton transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 575–590 (2002).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, “Integrable nonlinear Schrödinger systems and their soliton dynamics,” Dyn. Partial Differ. Equ. 1, 239–299 (2004).

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “On the design of NFT-based communication systems with lumped amplification,” J. Lightwave Technol. 35, 5464–5472 (2017).

[Crossref]

S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, “Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives,” Optica 4, 307–322 (2017).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

S. T. Le, I. D. Phillips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightwave Technol. 34, 2459–2466 (2016).

[Crossref]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express 23, 8317–8328 (2015).

[Crossref]

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett. 113, 013901 (2014).

[Crossref]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

O. C. Wright, “The Darboux transformation of some Manakov systems,” Appl. Math. Lett. 16, 647–652 (2003).

[Crossref]

C. Xie, M. Karlsson, P. A. Andrekson, H. Sunnerud, and J. Li, “Influences of polarization-mode dispersion on soliton transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 575–590 (2002).

[Crossref]

S. A. Derevyanko, J. E. Prilepsky, and D. A. Yakushev, “Statistics of a noise-driven Manakov soliton,” J. Phys. A 39, 1297–1309 (2006).

[Crossref]

J. Yang, “Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics,” Phys. Rev. E 59, 2393–2405 (1999).

[Crossref]

J.-W. Goossens, M. I. Yousefi, Y. Jaouën, and H. Hafermann, “Polarization-division multiplexing based on the nonlinear Fourier transform,” Opt. Express 25, 26437–26452 (2017).

[Crossref]

S. Hari, M. I. Yousefi, and F. R. Kschischang, “Multieigenvalue communication,” J. Lightwave Technol. 34, 3110–3117 (2016).

[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part III: spectrum modulation,” IEEE Trans. Inf. Theory 60, 4346–4369 (2014).

[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part I: mathematical tools,” IEEE Trans. Inf. Theory 60, 4312–4328 (2014).

[Crossref]

V. E. Zakharov and A. B. Shabat, “Exact theory of 2-dimensional self- focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Q. Zhang and T. H. Chan, “Noise models in the nonlinear spectral domain for optical fibre communications,” arXiv:1702.06226 (2017).

Q. Zhang and T. H. Chan, “A Gaussian noise model of spectral amplitudes in soliton communication systems,” in IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (IEEE, 2015), pp. 455–459.

Q. Zhang and T. H. Chan, “A spectral domain noise model for optical fibre channels,” in IEEE International Symposium on Information Theory, June2015, pp. 1660–1664.

S. Gaiarin, A. M. Perego, E. Porto da Silva, F. Da Ros, and D. Zibar, “Experimental demonstration of dual polarization nonlinear frequency division multiplexed optical transmission system,” in 43rd European Conference on Optical Communications (ECOC) (2017), paper W.3.C.2.

O. C. Wright, “The Darboux transformation of some Manakov systems,” Appl. Math. Lett. 16, 647–652 (2003).

[Crossref]

Y. Chen and H. Haus, “Manakov solitons and polarization mode dispersion,” Chaos 10, 529–538 (2000).

[Crossref]

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, “Integrable nonlinear Schrödinger systems and their soliton dynamics,” Dyn. Partial Differ. Equ. 1, 239–299 (2004).

C. Xie, M. Karlsson, P. A. Andrekson, H. Sunnerud, and J. Li, “Influences of polarization-mode dispersion on soliton transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 575–590 (2002).

[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part III: spectrum modulation,” IEEE Trans. Inf. Theory 60, 4346–4369 (2014).

[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part I: mathematical tools,” IEEE Trans. Inf. Theory 60, 4312–4328 (2014).

[Crossref]

A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightwave Technol. 11, 395–399 (1993).

[Crossref]

E. Ip and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26, 3416–3425 (2008).

[Crossref]

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for MQAM constellations,” J. Lightwave Technol. 27, 989–999 (2009).

[Crossref]

C. R. Menyuk and B. S. Marks, “Interaction of polarization mode dispersion and nonlinearity in optical fiber transmission systems,” J. Lightwave Technol. 24, 2806–2826 (2006).

[Crossref]

R. J. Essiambre, P. J. Kramer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28, 662–701 (2010).

[Crossref]

A. D. Ellis, M. Tan, M. A. Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvel, “4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightwave Technol. 34, 1717–1723 (2016).

[Crossref]

S. T. Le, I. D. Phillips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightwave Technol. 34, 2459–2466 (2016).

[Crossref]

S. Hari, M. I. Yousefi, and F. R. Kschischang, “Multieigenvalue communication,” J. Lightwave Technol. 34, 3110–3117 (2016).

[Crossref]

S. Hari and F. R. Kschischang, “Bi-directional algorithm for computing discrete spectral amplitudes in the NFT,” J. Lightwave Technol. 34, 3529–3537 (2016).

[Crossref]

H. Bülow, “Experimental demonstration of optical signal detection using nonlinear Fourier transform,” J. Lightwave Technol. 33, 1433–1439 (2015).

[Crossref]

T. Gui, T. H. Chan, C. Lu, A. P. T. Lau, and P. K. A. Wai, “Alternative decoding methods for optical communications based on nonlinear Fourier transform,” J. Lightwave Technol. 35, 1542–1550 (2017).

[Crossref]

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “On the design of NFT-based communication systems with lumped amplification,” J. Lightwave Technol. 35, 5464–5472 (2017).

[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).

[Crossref]

S. A. Derevyanko, J. E. Prilepsky, and D. A. Yakushev, “Statistics of a noise-driven Manakov soliton,” J. Phys. A 39, 1297–1309 (2006).

[Crossref]

S. T. Le, V. Aref, and H. Buelow, “Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 11, 570–576 (2017).

[Crossref]

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fiber communications,” Nature 411, 1027–1030 (2001).

[Crossref]

K. Kikuchi, “Analyses of wavelength-and polarization-division multiplexed transmission characteristics of optical quadrature-amplitude-modulation signals,” Opt. Express 19, 17985–17995 (2011).

[Crossref]

J.-W. Goossens, M. I. Yousefi, Y. Jaouën, and H. Hafermann, “Polarization-division multiplexing based on the nonlinear Fourier transform,” Opt. Express 25, 26437–26452 (2017).

[Crossref]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express 23, 8317–8328 (2015).

[Crossref]

J. Yang, “Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics,” Phys. Rev. E 59, 2393–2405 (1999).

[Crossref]

T. Lakoba and D. Kaup, “Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers,” Phys. Rev. E 56, 6147–6165 (1997).

[Crossref]

T. P. Horikis and J. N. Elgin, “Nonlinear optics in a birefringent optical fiber,” Phys. Rev. E 69, 016603 (2004).

[Crossref]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[Crossref]

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett. 113, 013901 (2014).

[Crossref]

R. G. Docksey and J. N. Elgin, “Closure of the Manakov system,” SIAM J. Math. Anal. 32, 54–79 (2000).

[Crossref]

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

V. E. Zakharov and A. B. Shabat, “Exact theory of 2-dimensional self- focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

N. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “The inverse scattering transform-Fourier analysis for nonlinear problems,” Stud. Appl. Math. 53, 249–315 (1974).

[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2013).

V. Aref, H. Bülow, K. Schuh, and W. Idler, “Experimental demonstration of nonlinear frequency division multiplexed transmission,” in 41st European Conference on Optical Communications (ECOC) (2015), paper Tu.1.1.2.

V. Aref, S. T. Le, and H. Buelow, “Demonstration of fully nonlinear spectrum modulated system in the highly nonlinear optical transmission regime,” in 42st European Conference on Optical Communications (ECOC) (2016), paper Th.3.B.2.

S. Gaiarin, A. M. Perego, E. Porto da Silva, F. Da Ros, and D. Zibar, “Experimental demonstration of dual polarization nonlinear frequency division multiplexed optical transmission system,” in 43rd European Conference on Optical Communications (ECOC) (2017), paper W.3.C.2.

A. Maruta and Y. Matsuda, “Polarization division multiplexed optical eigenvalue modulation,” in International Conference on Photonics in Switching (PS), Florence, Italy (2015), pp. 265–267.

V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer-Verlag, 1991).

A. Hasegawa and Y. Kodama, Solitons in Optical Communications, 7th ed. (Oxford University, 1995).

N. Nabavi and T. J. Hall, “Demultiplexing by independent component analysis in coherent optical transmission: the polarization channel alignment problem,” in Photonics North (2015).

Q. Zhang and T. H. Chan, “A Gaussian noise model of spectral amplitudes in soliton communication systems,” in IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (IEEE, 2015), pp. 455–459.

Q. Zhang and T. H. Chan, “A spectral domain noise model for optical fibre channels,” in IEEE International Symposium on Information Theory, June2015, pp. 1660–1664.

Q. Zhang and T. H. Chan, “Noise models in the nonlinear spectral domain for optical fibre communications,” arXiv:1702.06226 (2017).

V. Aref, “Control and detection of discrete spectral amplitudes in nonlinear Fourier spectrum,” arXiv:1605.06328 (2016).