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]

Q. Wang, J. Li, L. Zhang, and W. Xie, “Hermite-Gaussian-like soliton in the nonlocal nonlinear fractional Schrödinger equation,” Europhys. Lett. 122, 64001 (2018).

[Crossref]

X. Yao and X. Liu, “Off-site and on-site vortex solitons in space-fractional photonic lattices,” Opt. Lett. 43, 5749–5752 (2018).

[Crossref]

M. Chen, S. Zeng, D. Lu, W. Hu, and Q. Guo, “Optical solitons, self-focusing, and wave collapse in a space-fractional Schrödinger equation with a Kerr-type nonlinearity,” Phys. Rev. E 98, 022211 (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, H. Deng, W. Zhang, F. Ye, and L. Dong, “Fundamental solitons in the nonlinear fractional Schrödinger equation with a PT-symmetric potential,” Europhys. Lett. 122, 24002 (2018).

[Crossref]

X. Yao and X. Liu, “Solitons in the fractional Schrödinger equation with parity-time-symmetric lattice potential,” Photon. Res. 6, 875–879 (2018).

[Crossref]

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

[Crossref]

Y. Zhang, R. Wang, H. Zhong, J. Zhang, M. R. Belić, and Y. Zhang, “Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation,” Sci. Rep. 7, 17872 (2017).

[Crossref]

L. Zhang, Z. He, C. Conti, Z. Wang, Y. Hu, D. Lei, Y. Li, and D. Fan, “Modulational instability in fractional nonlinear Schrödinger equation,” Commun. Nonlinear Sci. Numer. Simul. 48, 531–540 (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]

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. Duo and Y. Zhang, “Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation,” Comput. Math. Appl. 71, 2257–2271 (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]

L. Li, X. Zhu, H. Li, and T. Lai, “Vector solitons in parity-time symmetric lattices with nonlocal nonlinearity,” J. Opt. 18, 095501 (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. Belic, 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]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5, 83–130 (2013).

[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]

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

[Crossref]

L. P. Rokhinson, X. Liu, and J. K. Furdyna, “The fractional a.c. Josephson effect in a semiconductor-superconductor nanowire as a signature of Majorana particles,” Nat. Phys. 8, 795–799 (2012).

[Crossref]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).

[Crossref]

C. E. Ruter, 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. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett. 103, 123601 (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 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]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).

[Crossref]

S. K. Adhikari and B. A. Malomed, “Tightly bound gap solitons in a Fermi gas,” Europhys. Lett. 79, 50003 (2007).

[Crossref]

T. Mayteevarunyoo and B. A. Malomed, “Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice,” Phys. Rev. A 74, 033616 (2006).

[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]

R. Metzler and J. Klafter, “The random walk’s guide to anomalous diffusion: a fractional dynamics approach,” Phys. Rep. 339, 1–77 (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]

R. B. Laughlin, “Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations,” Phys. Rev. Lett. 50, 1395–1398 (1983).

[Crossref]

S. K. Adhikari and B. A. Malomed, “Tightly bound gap solitons in a Fermi gas,” Europhys. Lett. 79, 50003 (2007).

[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, R. Wang, H. Zhong, J. Zhang, M. R. Belić, and Y. Zhang, “Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation,” Sci. Rep. 7, 17872 (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, 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. Belic, 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]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).

[Crossref]

M. Chen, S. Zeng, D. Lu, W. Hu, and Q. Guo, “Optical solitons, self-focusing, and wave collapse in a space-fractional Schrödinger equation with a Kerr-type nonlinearity,” Phys. Rev. E 98, 022211 (2018).

[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]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).

[Crossref]

C. E. Ruter, 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]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).

[Crossref]

L. Zhang, Z. He, C. Conti, Z. Wang, Y. Hu, D. Lei, Y. Li, and D. Fan, “Modulational instability in fractional nonlinear Schrödinger equation,” Commun. Nonlinear Sci. Numer. Simul. 48, 531–540 (2017).

[Crossref]

C. Huang, H. Deng, W. Zhang, F. Ye, and L. Dong, “Fundamental solitons in the nonlinear fractional Schrödinger equation with a PT-symmetric potential,” Europhys. Lett. 122, 24002 (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, H. Deng, W. Zhang, F. Ye, and L. Dong, “Fundamental solitons in the nonlinear fractional Schrödinger equation with a PT-symmetric potential,” Europhys. Lett. 122, 24002 (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 with an optical lattice,” 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]

S. Duo and Y. Zhang, “Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation,” Comput. Math. Appl. 71, 2257–2271 (2016).

[Crossref]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).

[Crossref]

C. E. Ruter, 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]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).

[Crossref]

L. Zhang, Z. He, C. Conti, Z. Wang, Y. Hu, D. Lei, Y. Li, and D. Fan, “Modulational instability in fractional nonlinear Schrödinger equation,” Commun. Nonlinear Sci. Numer. Simul. 48, 531–540 (2017).

[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]

L. P. Rokhinson, X. Liu, and J. K. Furdyna, “The fractional a.c. Josephson effect in a semiconductor-superconductor nanowire as a signature of Majorana particles,” Nat. Phys. 8, 795–799 (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]

M. Chen, S. Zeng, D. Lu, W. Hu, and Q. Guo, “Optical solitons, self-focusing, and wave collapse in a space-fractional Schrödinger equation with a Kerr-type nonlinearity,” Phys. Rev. E 98, 022211 (2018).

[Crossref]

L. Zhang, Z. He, C. Conti, Z. Wang, Y. Hu, D. Lei, Y. Li, and D. Fan, “Modulational instability in fractional nonlinear Schrödinger equation,” Commun. Nonlinear Sci. Numer. Simul. 48, 531–540 (2017).

[Crossref]

M. Chen, S. Zeng, D. Lu, W. Hu, and Q. Guo, “Optical solitons, self-focusing, and wave collapse in a space-fractional Schrödinger equation with a Kerr-type nonlinearity,” Phys. Rev. E 98, 022211 (2018).

[Crossref]

L. Zhang, Z. He, C. Conti, Z. Wang, Y. Hu, D. Lei, Y. Li, and D. Fan, “Modulational instability in fractional nonlinear Schrödinger equation,” Commun. Nonlinear Sci. Numer. Simul. 48, 531–540 (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]

C. Huang, H. Deng, W. Zhang, F. Ye, and L. Dong, “Fundamental solitons in the nonlinear fractional Schrödinger equation with a PT-symmetric potential,” Europhys. Lett. 122, 24002 (2018).

[Crossref]

C. Huang and L. Dong, “Beam propagation management in a fractional Schrödinger equation with an optical lattice,” 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]

C. E. Ruter, 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]

R. Metzler and J. Klafter, “The random walk’s guide to anomalous diffusion: a fractional dynamics approach,” Phys. Rep. 339, 1–77 (2000).

[Crossref]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).

[Crossref]

L. Li, X. Zhu, H. Li, and T. Lai, “Vector solitons in parity-time symmetric lattices with nonlocal nonlinearity,” J. Opt. 18, 095501 (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,” 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]

R. B. Laughlin, “Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations,” Phys. Rev. Lett. 50, 1395–1398 (1983).

[Crossref]

L. Zhang, Z. He, C. Conti, Z. Wang, Y. Hu, D. Lei, Y. Li, and D. Fan, “Modulational instability in fractional nonlinear Schrödinger equation,” Commun. Nonlinear Sci. Numer. Simul. 48, 531–540 (2017).

[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]

L. Li, X. Zhu, H. Li, and T. Lai, “Vector solitons in parity-time symmetric lattices with nonlocal nonlinearity,” J. Opt. 18, 095501 (2016).

[Crossref]

Q. Wang, J. Li, L. Zhang, and W. Xie, “Hermite-Gaussian-like soliton in the nonlocal nonlinear fractional Schrödinger equation,” Europhys. Lett. 122, 64001 (2018).

[Crossref]

L. Li, X. Zhu, H. Li, and T. Lai, “Vector solitons in parity-time symmetric lattices with nonlocal nonlinearity,” J. Opt. 18, 095501 (2016).

[Crossref]

L. Zhang, Z. He, C. Conti, Z. Wang, Y. Hu, D. Lei, Y. Li, and D. Fan, “Modulational instability in fractional nonlinear Schrödinger equation,” Commun. Nonlinear Sci. Numer. Simul. 48, 531–540 (2017).

[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]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).

[Crossref]

X. Yao and X. Liu, “Solitons in the fractional Schrödinger equation with parity-time-symmetric lattice potential,” Photon. Res. 6, 875–879 (2018).

[Crossref]

X. Yao and X. Liu, “Off-site and on-site vortex solitons in space-fractional photonic lattices,” Opt. Lett. 43, 5749–5752 (2018).

[Crossref]

Y. Zhang, X. Liu, M. R. Belic, 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. P. Rokhinson, X. Liu, and J. K. Furdyna, “The fractional a.c. Josephson effect in a semiconductor-superconductor nanowire as a signature of Majorana particles,” Nat. Phys. 8, 795–799 (2012).

[Crossref]

M. Chen, S. Zeng, D. Lu, W. Hu, and Q. Guo, “Optical solitons, self-focusing, and wave collapse in a space-fractional Schrödinger equation with a Kerr-type nonlinearity,” Phys. Rev. E 98, 022211 (2018).

[Crossref]

C. E. Ruter, 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]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).

[Crossref]

S. K. Adhikari and B. A. Malomed, “Tightly bound gap solitons in a Fermi gas,” Europhys. Lett. 79, 50003 (2007).

[Crossref]

T. Mayteevarunyoo and B. A. Malomed, “Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice,” Phys. Rev. A 74, 033616 (2006).

[Crossref]

T. Mayteevarunyoo and B. A. Malomed, “Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice,” Phys. Rev. A 74, 033616 (2006).

[Crossref]

R. Metzler and J. Klafter, “The random walk’s guide to anomalous diffusion: a fractional dynamics approach,” Phys. Rep. 339, 1–77 (2000).

[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]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).

[Crossref]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).

[Crossref]

L. P. Rokhinson, X. Liu, and J. K. Furdyna, “The fractional a.c. Josephson effect in a semiconductor-superconductor nanowire as a signature of Majorana particles,” Nat. Phys. 8, 795–799 (2012).

[Crossref]

C. E. Ruter, 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]

C. E. Ruter, 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]

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

[Crossref]

Q. Wang, J. Li, L. Zhang, and W. Xie, “Hermite-Gaussian-like soliton in the nonlocal nonlinear fractional Schrödinger equation,” Europhys. Lett. 122, 64001 (2018).

[Crossref]

Y. Zhang, R. Wang, H. Zhong, J. Zhang, M. R. Belić, and Y. Zhang, “Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation,” Sci. Rep. 7, 17872 (2017).

[Crossref]

L. Zhang, Z. He, C. Conti, Z. Wang, Y. Hu, D. Lei, Y. Li, and D. Fan, “Modulational instability in fractional nonlinear Schrödinger equation,” Commun. Nonlinear Sci. Numer. Simul. 48, 531–540 (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, 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. Belic, 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]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5, 83–130 (2013).

[Crossref]

Q. Wang, J. Li, L. Zhang, and W. Xie, “Hermite-Gaussian-like soliton in the nonlocal nonlinear fractional Schrödinger equation,” Europhys. Lett. 122, 64001 (2018).

[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).

[Crossref]

C. Huang, H. Deng, W. Zhang, F. Ye, and L. Dong, “Fundamental solitons in the nonlinear fractional Schrödinger equation with a PT-symmetric potential,” Europhys. Lett. 122, 24002 (2018).

[Crossref]

M. Chen, S. Zeng, D. Lu, W. Hu, and Q. Guo, “Optical solitons, self-focusing, and wave collapse in a space-fractional Schrödinger equation with a Kerr-type nonlinearity,” Phys. Rev. E 98, 022211 (2018).

[Crossref]

Y. Zhang, R. Wang, H. Zhong, J. Zhang, M. R. Belić, and Y. Zhang, “Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation,” Sci. Rep. 7, 17872 (2017).

[Crossref]

Q. Wang, J. Li, L. Zhang, and W. Xie, “Hermite-Gaussian-like soliton in the nonlocal nonlinear fractional Schrödinger equation,” Europhys. Lett. 122, 64001 (2018).

[Crossref]

L. Zhang, Z. He, C. Conti, Z. Wang, Y. Hu, D. Lei, Y. Li, and D. Fan, “Modulational instability in fractional nonlinear Schrödinger equation,” Commun. Nonlinear Sci. Numer. Simul. 48, 531–540 (2017).

[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]

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