J. Xiao, Z. Tian, C. Huang, and L. Dong, “Surface gap solitons in a nonlinear fractional Schrödinger equation,” Opt. Express 26, 2650–2658 (2018).

[Crossref]

L. Dong and C. Huang, “Double-hump solitons in fractional dimensions with a PT-symmetric potential,” Opt. Express 26, 10509–10518 (2018).

[Crossref]

X. M. Liu, X. K. Yao, and Y. D. Cui, “Real-time dynamics of the build-up of solitons in mode-locked lasers,” Phys. Rev. Lett. 121, 023905 (2018).

X. K. Yao and X. M. Liu, “Beam dynamics in disordered PT-symmetric optical lattices based on eigenstate analyses,” Phys. Rev. A 95, 033804 (2017).

[Crossref]

C. Huang and L. Dong, “Beam propagation management in a fractional Schrödinger equation,” Sci. Rep. 7, 5442 (2017).

[Crossref]

X. Huang, X. Shi, Z. Deng, Y. Bai, and X. Fu, “Potential barrier-induced dynamics of finite energy Airy beams in fractional Schrödinger equation,” Opt. Express 25, 32560–32569 (2017).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, “Diffraction-free beams in fractional Schrödinger equation,” Sci. Rep. 6, 23645 (2016).

[Crossref]

Q. Li and X. Wu, “Soliton solutions for fractional Schrödinger equations,” Appl. Math. Lett. 53, 119–124 (2016).

[Crossref]

Y. Wan and Z. Wang, “Bound state for fractional Schrödinger equation with saturable nonlinearity,” Appl. Math. Comput. 273, 735–740 (2016).

[Crossref]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41, 5636–5639 (2016).

[Crossref]

L. Zhang, C. Li, H. Zhong, C. Xu, D. Lei, Y. Li, and D. Fan, “Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes,” Opt. Express 24, 14406–14418 (2016).

[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).

[Crossref]

Y. V. Kartashov, C. Hang, G. Huang, and L. Torner, “Three-dimensional topological solitons in PT-symmetric optical lattices,” Optica 3, 1048–1055 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

S. Longhi, “Fractional Schrödinger equation in optics,” Opt. Lett. 40, 1117–1120 (2015).

[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).

[Crossref]

B. A. Stickler, “Potential condensed-matter realization of space-fractional quantum mechanics: the one-dimensional Lévy crystal,” Phys. Rev. E 88, 012120 (2013).

[Crossref]

Y. Lumer, Y. Plotnik, M. C. Rechtsman, and M. Segev, “Nonlinearly induced PT transition in photonic systems,” Phys. Rev. Lett. 111, 263901 (2013).

[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).

[Crossref]

B. Guo and D. Huang, “Existence and stability of standing waves for nonlinear fractional Schrödinger equations,” J. Math. Phys. 53, 083702 (2012).

[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).

[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, G. Siviloglou, and D. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT-symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[Crossref]

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 227, 6862–6876 (2008).

[Crossref]

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118, 153–197 (2007).

[Crossref]

N. Laskin, “Fractional Schrödinger equation,” Phys. Rev. E 66, 056108 (2002).

[Crossref]

N. Laskin, “Fractional quantum mechanics,” Phys. Rev. E 62, 3135–3145 (2000).

[Crossref]

N. Laskin, “Fractional quantum mechanics and Lévy path integrals,” Phys. Lett. A 268, 298–305 (2000).

[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, “Diffraction-free beams in fractional Schrödinger equation,” Sci. Rep. 6, 23645 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, “Diffraction-free beams in fractional Schrödinger equation,” Sci. Rep. 6, 23645 (2016).

[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).

[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).

[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).

[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, G. Siviloglou, and D. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT-symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]

X. M. Liu, X. K. Yao, and Y. D. Cui, “Real-time dynamics of the build-up of solitons in mode-locked lasers,” Phys. Rev. Lett. 121, 023905 (2018).

S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).

[Crossref]

J. Xiao, Z. Tian, C. Huang, and L. Dong, “Surface gap solitons in a nonlinear fractional Schrödinger equation,” Opt. Express 26, 2650–2658 (2018).

[Crossref]

L. Dong and C. Huang, “Double-hump solitons in fractional dimensions with a PT-symmetric potential,” Opt. Express 26, 10509–10518 (2018).

[Crossref]

C. Huang and L. Dong, “Beam propagation management in a fractional Schrödinger equation,” Sci. Rep. 7, 5442 (2017).

[Crossref]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41, 5636–5639 (2016).

[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, G. Siviloglou, and D. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).

[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT-symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).

[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, G. Siviloglou, and D. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).

[Crossref]

B. Guo and D. Huang, “Existence and stability of standing waves for nonlinear fractional Schrödinger equations,” J. Math. Phys. 53, 083702 (2012).

[Crossref]

R. Herrmann, Fractional Calculus: An Introduction for Physicists (World Scientific, 2011).

L. Dong and C. Huang, “Double-hump solitons in fractional dimensions with a PT-symmetric potential,” Opt. Express 26, 10509–10518 (2018).

[Crossref]

J. Xiao, Z. Tian, C. Huang, and L. Dong, “Surface gap solitons in a nonlinear fractional Schrödinger equation,” Opt. Express 26, 2650–2658 (2018).

[Crossref]

C. Huang and L. Dong, “Beam propagation management in a fractional Schrödinger equation,” Sci. Rep. 7, 5442 (2017).

[Crossref]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41, 5636–5639 (2016).

[Crossref]

B. Guo and D. Huang, “Existence and stability of standing waves for nonlinear fractional Schrödinger equations,” J. Math. Phys. 53, 083702 (2012).

[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).

[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).

[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).

[Crossref]

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118, 153–197 (2007).

[Crossref]

N. Laskin, “Fractional Schrödinger equation,” Phys. Rev. E 66, 056108 (2002).

[Crossref]

N. Laskin, “Fractional quantum mechanics and Lévy path integrals,” Phys. Lett. A 268, 298–305 (2000).

[Crossref]

N. Laskin, “Fractional quantum mechanics,” Phys. Rev. E 62, 3135–3145 (2000).

[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).

[Crossref]

Q. Li and X. Wu, “Soliton solutions for fractional Schrödinger equations,” Appl. Math. Lett. 53, 119–124 (2016).

[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).

[Crossref]

X. M. Liu, X. K. Yao, and Y. D. Cui, “Real-time dynamics of the build-up of solitons in mode-locked lasers,” Phys. Rev. Lett. 121, 023905 (2018).

X. K. Yao and X. M. Liu, “Beam dynamics in disordered PT-symmetric optical lattices based on eigenstate analyses,” Phys. Rev. A 95, 033804 (2017).

[Crossref]

Y. Lumer, Y. Plotnik, M. C. Rechtsman, and M. Segev, “Nonlinearly induced PT transition in photonic systems,” Phys. Rev. Lett. 111, 263901 (2013).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).

[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT-symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, G. Siviloglou, and D. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT-symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).

[Crossref]

Y. Lumer, Y. Plotnik, M. C. Rechtsman, and M. Segev, “Nonlinearly induced PT transition in photonic systems,” Phys. Rev. Lett. 111, 263901 (2013).

[Crossref]

Y. Lumer, Y. Plotnik, M. C. Rechtsman, and M. Segev, “Nonlinearly induced PT transition in photonic systems,” Phys. Rev. Lett. 111, 263901 (2013).

[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).

[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, G. Siviloglou, and D. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).

[Crossref]

Y. Lumer, Y. Plotnik, M. C. Rechtsman, and M. Segev, “Nonlinearly induced PT transition in photonic systems,” Phys. Rev. Lett. 111, 263901 (2013).

[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).

[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, G. Siviloglou, and D. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).

[Crossref]

B. A. Stickler, “Potential condensed-matter realization of space-fractional quantum mechanics: the one-dimensional Lévy crystal,” Phys. Rev. E 88, 012120 (2013).

[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).

[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).

[Crossref]

Y. Wan and Z. Wang, “Bound state for fractional Schrödinger equation with saturable nonlinearity,” Appl. Math. Comput. 273, 735–740 (2016).

[Crossref]

Y. Wan and Z. Wang, “Bound state for fractional Schrödinger equation with saturable nonlinearity,” Appl. Math. Comput. 273, 735–740 (2016).

[Crossref]

Q. Li and X. Wu, “Soliton solutions for fractional Schrödinger equations,” Appl. Math. Lett. 53, 119–124 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, “Diffraction-free beams in fractional Schrödinger equation,” Sci. Rep. 6, 23645 (2016).

[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).

[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).

[Crossref]

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 227, 6862–6876 (2008).

[Crossref]

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118, 153–197 (2007).

[Crossref]

J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010).

X. M. Liu, X. K. Yao, and Y. D. Cui, “Real-time dynamics of the build-up of solitons in mode-locked lasers,” Phys. Rev. Lett. 121, 023905 (2018).

X. K. Yao and X. M. Liu, “Beam dynamics in disordered PT-symmetric optical lattices based on eigenstate analyses,” Phys. Rev. A 95, 033804 (2017).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, “Diffraction-free beams in fractional Schrödinger equation,” Sci. Rep. 6, 23645 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, “Diffraction-free beams in fractional Schrödinger equation,” Sci. Rep. 6, 23645 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).

[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).

[Crossref]

L. Zhang, C. Li, H. Zhong, C. Xu, D. Lei, Y. Li, and D. Fan, “Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes,” Opt. Express 24, 14406–14418 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, “Diffraction-free beams in fractional Schrödinger equation,” Sci. Rep. 6, 23645 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

Y. Wan and Z. Wang, “Bound state for fractional Schrödinger equation with saturable nonlinearity,” Appl. Math. Comput. 273, 735–740 (2016).

[Crossref]

Q. Li and X. Wu, “Soliton solutions for fractional Schrödinger equations,” Appl. Math. Lett. 53, 119–124 (2016).

[Crossref]

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 227, 6862–6876 (2008).

[Crossref]

B. Guo and D. Huang, “Existence and stability of standing waves for nonlinear fractional Schrödinger equations,” J. Math. Phys. 53, 083702 (2012).

[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “PT symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).

[Crossref]

L. Zhang, C. Li, H. Zhong, C. Xu, D. Lei, Y. Li, and D. Fan, “Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes,” Opt. Express 24, 14406–14418 (2016).

[Crossref]

X. Huang, X. Shi, Z. Deng, Y. Bai, and X. Fu, “Potential barrier-induced dynamics of finite energy Airy beams in fractional Schrödinger equation,” Opt. Express 25, 32560–32569 (2017).

[Crossref]

J. Xiao, Z. Tian, C. Huang, and L. Dong, “Surface gap solitons in a nonlinear fractional Schrödinger equation,” Opt. Express 26, 2650–2658 (2018).

[Crossref]

L. Dong and C. Huang, “Double-hump solitons in fractional dimensions with a PT-symmetric potential,” Opt. Express 26, 10509–10518 (2018).

[Crossref]

N. Laskin, “Fractional quantum mechanics and Lévy path integrals,” Phys. Lett. A 268, 298–305 (2000).

[Crossref]

X. K. Yao and X. M. Liu, “Beam dynamics in disordered PT-symmetric optical lattices based on eigenstate analyses,” Phys. Rev. A 95, 033804 (2017).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).

[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).

[Crossref]

N. Laskin, “Fractional Schrödinger equation,” Phys. Rev. E 66, 056108 (2002).

[Crossref]

B. A. Stickler, “Potential condensed-matter realization of space-fractional quantum mechanics: the one-dimensional Lévy crystal,” Phys. Rev. E 88, 012120 (2013).

[Crossref]

N. Laskin, “Fractional quantum mechanics,” Phys. Rev. E 62, 3135–3145 (2000).

[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, G. Siviloglou, and D. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).

[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT-symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang, and M. Xiao, “Propagation dynamics of a light beam in a fractional Schrödinger equation,” Phys. Rev. Lett. 115, 180403 (2015).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).

[Crossref]

X. M. Liu, X. K. Yao, and Y. D. Cui, “Real-time dynamics of the build-up of solitons in mode-locked lasers,” Phys. Rev. Lett. 121, 023905 (2018).

Y. Lumer, Y. Plotnik, M. C. Rechtsman, and M. Segev, “Nonlinearly induced PT transition in photonic systems,” Phys. Rev. Lett. 111, 263901 (2013).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, “Diffraction-free beams in fractional Schrödinger equation,” Sci. Rep. 6, 23645 (2016).

[Crossref]

C. Huang and L. Dong, “Beam propagation management in a fractional Schrödinger equation,” Sci. Rep. 7, 5442 (2017).

[Crossref]

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118, 153–197 (2007).

[Crossref]

J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010).

R. Herrmann, Fractional Calculus: An Introduction for Physicists (World Scientific, 2011).