Symmetric and Anti-Symmetric Solitons of the Fractional Second- and Third-Order Nonlinear Schr?dinger Equation
Qi-Hao Cao and Chao-Qing Dai*
College of Optical, Mechanical and Electrical Engineering, Zhejiang A&F University, Lin'an 311300, China
Abstract :The fractional second- and third-order nonlinear Schrödinger equation is studied, symmetric and antisymmetric soliton solutions are derived, and the influence of the Lévy index on different solitons is analyzed. The stability and stability interval of solitons are discussed. The anti-interference ability of stable solitons to the small disturbance shows a good robustness.
收稿日期: 2021-07-14
出版日期: 2021-09-02
:
05.45.Yv
(Solitons)
42.65.Tg
(Optical solitons; nonlinear guided waves)
42.81.Dp
(Propagation, scattering, and losses; solitons)
[1] Kivshar Y S and Luther-Davies B 1998 Phys. Rep. 298 81
[2] Yu W T, Zhou Q, Mirzazadeh M, Liu W J, and Biswas A 2019 J. Adv. Res. 15 69
[3] Wen L, Guo H, Wang Y J, Hu A Y, Saito H, Dai C Q, and Zhang X F 2020 Phys. Rev. A 101 33610
[4] Li H, Liu C, Yang Z Y, and Yang W L 2020 Chin. Phys. Lett. 37 030302
[5] Wang B, Zhang Z, and Li B 2020 Chin. Phys. Lett. 37 030501
[6] Wang W, Yao R X, and Lou S Y 2020 Chin. Phys. Lett. 37 100501
[7] Fang Y, Wu G Z, Wang Y Y, and Dai C Q 2021 Nonlinear Dyn. 105 603
[8] Wang D S, Guo B, and Wang X L 2019 J. Differ. Eq. 266 5209
[9] Dai C Q and Wang Y Y 2020 Nonlinear Dyn. 102 1733
[10] Liu X Y, Zhou Q, Biswas A, Alzahrani A K, and Liu W J 2020 J. Adv. Res. 24 167
[11] Dong L, Qi W, Peng P, Wang L, and Huang C 2020 Nonlinear Dyn. 102 303
[12] Zhao L C, Qin Y H, Wang W L, and Yang Z Y 2020 Chin. Phys. Lett. 37 050502
[13] Wang B H, Wang Y Y, Dai C Q, and Chen Y X 2020 Alexandria Eng. J. 59 4699
[14] Longhi S 2015 Opt. Lett. 40 1117
[15] Li P F, Li R J, and Dai C Q 2021 Opt. Express 29 3193
[16] Li P F, Malomed B A, and Mihalache D 2020 Chaos Solitons & Fractals 132 109602
[17] Griesmaier A, Stuhler J, Koch T, Fattori M, Pfau T, Giovanazzi S 2006 Phys. Rev. Lett. 97 250402
[18] Marco P, Claudio C, Gaetano A, Antonio D L, and Cesare U 2004 Nature 432 733
[19] Mihalache D, Mazilu D, Lederer F, Crasovan L C, Kartashov Y V, Torner L, and Malomed B A 2006 Phys. Rev. E 74 066614
[20] Esbensen B K, Wlotzka A, Bache M, Bang O, and Krolikowski W 2011 Phys. Rev. A 84 053854
[1]
. [J]. 中国物理快报, 2023, 40(7): 70501-.
[2]
. [J]. 中国物理快报, 2023, 40(4): 40501-.
[3]
. [J]. 中国物理快报, 2023, 40(2): 20201-.
[4]
. [J]. 中国物理快报, 2022, 39(11): 114202-.
[5]
. [J]. 中国物理快报, 2022, 39(10): 100201-.
[6]
. [J]. 中国物理快报, 2022, 39(9): 94201-094201.
[7]
. [J]. 中国物理快报, 2022, 39(4): 44202-.
[8]
. [J]. 中国物理快报, 2022, 39(3): 34202-.
[9]
. [J]. 中国物理快报, 2022, 39(2): 20501-.
[10]
. [J]. 中国物理快报, 2022, 39(1): 10501-.
[11]
. [J]. 中国物理快报, 2021, 38(9): 90201-.
[12]
. [J]. 中国物理快报, 2021, 38(9): 94201-.
[13]
. [J]. 中国物理快报, 2021, 38(8): 80201-.
[14]
. [J]. 中国物理快报, 2021, 38(6): 60501-.
[15]
. [J]. 中国物理快报, 2020, 37(10): 100501-.