L. Dong and Z. Tian, “Truncated-Bloch-wave solitons in nonlinear fractional periodic systems,” Ann. Phys. 404, 57–65 (2019).

[Crossref]

L. Zeng and J. Zeng, “One-dimensional solitons in fractional Schrödinger equation with a spatially periodical modulated nonlinearity: nonlinear lattice,” Opt. Lett. 44(11), 2661–2664 (2019).

[Crossref]

J. Xie, X. Zhu, and Y. He, “Vector solitons in nonlinear fractional Schrödinger equations with parity-time-symmetric optical lattices,” Nonlinear Dyn. 97(2), 1287–1294 (2019).

[Crossref]

C. Huang and L. Dong, “Dissipative surface solitons in a nonlinear fractional Schrödinger equation,” Opt. Lett. 44(22), 5438–5441 (2019).

[Crossref]

L. Dong, C. Huang, and W. Qi, “Nonlocal solitons in fractional dimensions,” Opt. Lett. 44(20), 4917–4920 (2019).

[Crossref]

J. Xiao, Z. Tian, C. Huang, and L. Dong, “Surface gap solitons in a nonlinear fractional Schrödinger equation,” Opt. Express 26(3), 2650–2658 (2018).

[Crossref]

X. Yao and X. Liu, “Off-site and on-site vortex solitons in space-fractional photonic lattices,” Opt. Lett. 43(23), 5749–5752 (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(2), 24002 (2018).

[Crossref]

X. Yao and X. Liu, “Solitons in the fractional Schrödinger equation with parity-time-symmetric lattice potential,” Photonics Res. 6(9), 875–879 (2018).

[Crossref]

L. Dong and C. Huang, “Double-hump solitons in fractional dimensions with a PT-symmetric potential,” Opt. Express 26(8), 10509–10518 (2018).

[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(13), 14406–14418 (2016).

[Crossref]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41(24), 5636–5639 (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 Photonics Rev. 10(3), 526–531 (2016).

[Crossref]

S. Longhi, “Fractional Schrödinger equation in optics,” Opt. Lett. 40(6), 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(18), 180403 (2015).

[Crossref]

M. Wimmer, A. Regensburger, M.-A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6(1), 7782 (2015).

[Crossref]

C. Hang, Y. V. Kartashov, G. Huang, and V. V. Konotop, “Localization of light in a parity-time-symmetric quasi-periodic lattice,” Opt. Lett. 40(12), 2758–2761 (2015).

[Crossref]

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89(1), 013812 (2014).

[Crossref]

Y. V. Kartashov, “Vector solitons in parity-time-symmetric lattices,” Opt. Lett. 38(14), 2600–2603 (2013).

[Crossref]

C. Huang, C. Li, and L. Dong, “Stabilization of multipole-mode solitons in mixed linear-nonlinear lattices with a PT symmetry,” Opt. Express 21(3), 3917–3925 (2013).

[Crossref]

X. Zhu, H. Li, H. Wang, and Y. He, “Nonlocal multihump solitons in parity-time symmetric periodic potentials,” J. Opt. Soc. Am. B 30(7), 1987–1995 (2013).

[Crossref]

X. Zhu, H. Wang, H. Li, W. He, and Y. He, “Two-dimensional multipeak gap solitons supported by parity-time-symmetric periodic potentials,” Opt. Lett. 38(15), 2723–2725 (2013).

[Crossref]

Y. V. Bludov, V. V. Konotop, and B. A. Malomed, “Stable dark solitons in PT-symmetric dual-core waveguides,” Phys. Rev. A 87(1), 013816 (2013).

[Crossref]

C. Li, H. Liu, and L. Dong, “Multi-stable solitons in PT-symmetric optical lattices,” Opt. Express 20(15), 16823–16831 (2012).

[Crossref]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in PT-symmetric optical lattices,” Opt. Lett. 37(21), 4543–4545 (2012).

[Crossref]

V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-González, “Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions,” Phys. Rev. A 86(1), 013808 (2012).

[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85(2), 023822 (2012).

[Crossref]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85(1), 013831 (2012).

[Crossref]

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85(4), 043826 (2012).

[Crossref]

H. Li, X. Jiang, X. Zhu, and Z. Shi, “Nonlocal solitons in dual-periodic PT-symmetric optical lattices,” Phys. Rev. A 86(2), 023840 (2012).

[Crossref]

R. Driben and B. A. Malomed, “Stability of solitons in parity-time-symmetric couplers,” Opt. Lett. 36(22), 4323–4325 (2011).

[Crossref]

X. Zhu, H. Wang, L.-X. Zheng, H. Li, and Y.-J. He, “Gap solitons in parity-time complex periodic optical lattices with the real part of superlattices,” Opt. Lett. 36(14), 2680–2682 (2011).

[Crossref]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83(4), 041805 (2011).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. EI-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 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(2), 153–197 (2007).

[Crossref]

N. Laskin, “Fractional Schrödinger equation,” Phys. Rev. E 66(5), 056108 (2002).

[Crossref]

N. Laskin, “Fractional quantum mechanics and Lévy path integrals,” Phys. Lett. A 268(4-6), 298–305 (2000).

[Crossref]

N. Laskin, “Fractional quantum mechanics,” Phys. Rev. E 62(3), 3135–3145 (2000).

[Crossref]

C. M. Bender, S. Boettcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40(5), 2201–2229 (1999).

[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).

[Crossref]

F. Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Physik 52(7-8), 555–600 (1929).

[Crossref]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83(4), 041805 (2011).

[Crossref]

V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-González, “Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions,” Phys. Rev. A 86(1), 013808 (2012).

[Crossref]

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89(1), 013812 (2014).

[Crossref]

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89(1), 013812 (2014).

[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 Photonics Rev. 10(3), 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(18), 180403 (2015).

[Crossref]

C. M. Bender, S. Boettcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40(5), 2201–2229 (1999).

[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).

[Crossref]

M. Wimmer, A. Regensburger, M.-A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6(1), 7782 (2015).

[Crossref]

F. Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Physik 52(7-8), 555–600 (1929).

[Crossref]

Y. V. Bludov, V. V. Konotop, and B. A. Malomed, “Stable dark solitons in PT-symmetric dual-core waveguides,” Phys. Rev. A 87(1), 013816 (2013).

[Crossref]

C. M. Bender, S. Boettcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40(5), 2201–2229 (1999).

[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).

[Crossref]

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89(1), 013812 (2014).

[Crossref]

V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-González, “Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions,” Phys. Rev. A 86(1), 013808 (2012).

[Crossref]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85(1), 013831 (2012).

[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 Photonics Rev. 10(3), 526–531 (2016).

[Crossref]

M. Wimmer, A. Regensburger, M.-A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6(1), 7782 (2015).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. EI-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).

[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(2), 24002 (2018).

[Crossref]

L. Dong and Z. Tian, “Truncated-Bloch-wave solitons in nonlinear fractional periodic systems,” Ann. Phys. 404, 57–65 (2019).

[Crossref]

L. Dong, C. Huang, and W. Qi, “Nonlocal solitons in fractional dimensions,” Opt. Lett. 44(20), 4917–4920 (2019).

[Crossref]

C. Huang and L. Dong, “Dissipative surface solitons in a nonlinear fractional Schrödinger equation,” Opt. Lett. 44(22), 5438–5441 (2019).

[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(2), 24002 (2018).

[Crossref]

J. Xiao, Z. Tian, C. Huang, and L. Dong, “Surface gap solitons in a nonlinear fractional Schrödinger equation,” Opt. Express 26(3), 2650–2658 (2018).

[Crossref]

L. Dong and C. Huang, “Double-hump solitons in fractional dimensions with a PT-symmetric potential,” Opt. Express 26(8), 10509–10518 (2018).

[Crossref]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41(24), 5636–5639 (2016).

[Crossref]

C. Huang, C. Li, and L. Dong, “Stabilization of multipole-mode solitons in mixed linear-nonlinear lattices with a PT symmetry,” Opt. Express 21(3), 3917–3925 (2013).

[Crossref]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in PT-symmetric optical lattices,” Opt. Lett. 37(21), 4543–4545 (2012).

[Crossref]

C. Li, H. Liu, and L. Dong, “Multi-stable solitons in PT-symmetric optical lattices,” Opt. Express 20(15), 16823–16831 (2012).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. EI-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).

[Crossref]

V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-González, “Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions,” Phys. Rev. A 86(1), 013808 (2012).

[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85(2), 023822 (2012).

[Crossref]

J. Xie, X. Zhu, and Y. He, “Vector solitons in nonlinear fractional Schrödinger equations with parity-time-symmetric optical lattices,” Nonlinear Dyn. 97(2), 1287–1294 (2019).

[Crossref]

X. Zhu, H. Wang, H. Li, W. He, and Y. He, “Two-dimensional multipeak gap solitons supported by parity-time-symmetric periodic potentials,” Opt. Lett. 38(15), 2723–2725 (2013).

[Crossref]

X. Zhu, H. Li, H. Wang, and Y. He, “Nonlocal multihump solitons in parity-time symmetric periodic potentials,” J. Opt. Soc. Am. B 30(7), 1987–1995 (2013).

[Crossref]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85(1), 013831 (2012).

[Crossref]

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85(4), 043826 (2012).

[Crossref]

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85(4), 043826 (2012).

[Crossref]

L. Dong, C. Huang, and W. Qi, “Nonlocal solitons in fractional dimensions,” Opt. Lett. 44(20), 4917–4920 (2019).

[Crossref]

C. Huang and L. Dong, “Dissipative surface solitons in a nonlinear fractional Schrödinger equation,” Opt. Lett. 44(22), 5438–5441 (2019).

[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(2), 24002 (2018).

[Crossref]

L. Dong and C. Huang, “Double-hump solitons in fractional dimensions with a PT-symmetric potential,” Opt. Express 26(8), 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(3), 2650–2658 (2018).

[Crossref]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41(24), 5636–5639 (2016).

[Crossref]

C. Huang, C. Li, and L. Dong, “Stabilization of multipole-mode solitons in mixed linear-nonlinear lattices with a PT symmetry,” Opt. Express 21(3), 3917–3925 (2013).

[Crossref]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in PT-symmetric optical lattices,” Opt. Lett. 37(21), 4543–4545 (2012).

[Crossref]

H. Li, X. Jiang, X. Zhu, and Z. Shi, “Nonlocal solitons in dual-periodic PT-symmetric optical lattices,” Phys. Rev. A 86(2), 023840 (2012).

[Crossref]

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89(1), 013812 (2014).

[Crossref]

C. Hang, Y. V. Kartashov, G. Huang, and V. V. Konotop, “Localization of light in a parity-time-symmetric quasi-periodic lattice,” Opt. Lett. 40(12), 2758–2761 (2015).

[Crossref]

Y. V. Kartashov, “Vector solitons in parity-time-symmetric lattices,” Opt. Lett. 38(14), 2600–2603 (2013).

[Crossref]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83(4), 041805 (2011).

[Crossref]

V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-González, “Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions,” Phys. Rev. A 86(1), 013808 (2012).

[Crossref]

C. Hang, Y. V. Kartashov, G. Huang, and V. V. Konotop, “Localization of light in a parity-time-symmetric quasi-periodic lattice,” Opt. Lett. 40(12), 2758–2761 (2015).

[Crossref]

Y. V. Bludov, V. V. Konotop, and B. A. Malomed, “Stable dark solitons in PT-symmetric dual-core waveguides,” Phys. Rev. A 87(1), 013816 (2013).

[Crossref]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83(4), 041805 (2011).

[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(2), 153–197 (2007).

[Crossref]

N. Laskin, “Fractional Schrödinger equation,” Phys. Rev. E 66(5), 056108 (2002).

[Crossref]

N. Laskin, “Fractional quantum mechanics and Lévy path integrals,” Phys. Lett. A 268(4-6), 298–305 (2000).

[Crossref]

N. Laskin, “Fractional quantum mechanics,” Phys. Rev. E 62(3), 3135–3145 (2000).

[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(13), 14406–14418 (2016).

[Crossref]

C. Huang, C. Li, and L. Dong, “Stabilization of multipole-mode solitons in mixed linear-nonlinear lattices with a PT symmetry,” Opt. Express 21(3), 3917–3925 (2013).

[Crossref]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in PT-symmetric optical lattices,” Opt. Lett. 37(21), 4543–4545 (2012).

[Crossref]

C. Li, H. Liu, and L. Dong, “Multi-stable solitons in PT-symmetric optical lattices,” Opt. Express 20(15), 16823–16831 (2012).

[Crossref]

X. Zhu, H. Li, H. Wang, and Y. He, “Nonlocal multihump solitons in parity-time symmetric periodic potentials,” J. Opt. Soc. Am. B 30(7), 1987–1995 (2013).

[Crossref]

X. Zhu, H. Wang, H. Li, W. He, and Y. He, “Two-dimensional multipeak gap solitons supported by parity-time-symmetric periodic potentials,” Opt. Lett. 38(15), 2723–2725 (2013).

[Crossref]

H. Li, X. Jiang, X. Zhu, and Z. Shi, “Nonlocal solitons in dual-periodic PT-symmetric optical lattices,” Phys. Rev. A 86(2), 023840 (2012).

[Crossref]

X. Zhu, H. Wang, L.-X. Zheng, H. Li, and Y.-J. He, “Gap solitons in parity-time complex periodic optical lattices with the real part of superlattices,” Opt. Lett. 36(14), 2680–2682 (2011).

[Crossref]

C. Li, H. Liu, and L. Dong, “Multi-stable solitons in PT-symmetric optical lattices,” Opt. Express 20(15), 16823–16831 (2012).

[Crossref]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in PT-symmetric optical lattices,” Opt. Lett. 37(21), 4543–4545 (2012).

[Crossref]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85(1), 013831 (2012).

[Crossref]

X. Yao and X. Liu, “Solitons in the fractional Schrödinger equation with parity-time-symmetric lattice potential,” Photonics Res. 6(9), 875–879 (2018).

[Crossref]

X. Yao and X. Liu, “Off-site and on-site vortex solitons in space-fractional photonic lattices,” Opt. Lett. 43(23), 5749–5752 (2018).

[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(18), 180403 (2015).

[Crossref]

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85(4), 043826 (2012).

[Crossref]

S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85(4), 043826 (2012).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. EI-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).

[Crossref]

C. M. Bender, S. Boettcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40(5), 2201–2229 (1999).

[Crossref]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85(1), 013831 (2012).

[Crossref]

M. Wimmer, A. Regensburger, M.-A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6(1), 7782 (2015).

[Crossref]

Z. H. Musslimani, K. G. Makris, R. EI-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100(3), 030402 (2008).

[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85(2), 023822 (2012).

[Crossref]

M. Wimmer, A. Regensburger, M.-A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6(1), 7782 (2015).

[Crossref]

M. Wimmer, A. Regensburger, M.-A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6(1), 7782 (2015).

[Crossref]

H. Li, X. Jiang, X. Zhu, and Z. Shi, “Nonlocal solitons in dual-periodic PT-symmetric optical lattices,” Phys. Rev. A 86(2), 023840 (2012).

[Crossref]

X. Zhu, H. Li, H. Wang, and Y. He, “Nonlocal multihump solitons in parity-time symmetric periodic potentials,” J. Opt. Soc. Am. B 30(7), 1987–1995 (2013).

[Crossref]

X. Zhu, H. Wang, H. Li, W. He, and Y. He, “Two-dimensional multipeak gap solitons supported by parity-time-symmetric periodic potentials,” Opt. Lett. 38(15), 2723–2725 (2013).

[Crossref]

X. Zhu, H. Wang, L.-X. Zheng, H. Li, and Y.-J. He, “Gap solitons in parity-time complex periodic optical lattices with the real part of superlattices,” Opt. Lett. 36(14), 2680–2682 (2011).

[Crossref]

M. Wimmer, A. Regensburger, M.-A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6(1), 7782 (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 Photonics Rev. 10(3), 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(18), 180403 (2015).

[Crossref]

J. Xie, X. Zhu, and Y. He, “Vector solitons in nonlinear fractional Schrödinger equations with parity-time-symmetric optical lattices,” Nonlinear Dyn. 97(2), 1287–1294 (2019).

[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85(2), 023822 (2012).

[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(2), 153–197 (2007).

[Crossref]

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

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