Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions

doi:10.1088/1674-1056/ad6258

中国物理B ›› 2024, Vol. 33 ›› Issue (9): 90207-090207.doi: 10.1088/1674-1056/ad6258

Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions

Luyao Zhang(张路瑶) and Xiyang Xie(解西阳)†

Department of Mathematics and Physics, Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China

收稿日期:2024-06-27 修回日期:2024-07-07 接受日期:2024-07-12 出版日期:2024-09-15 发布日期:2024-08-30
通讯作者: Xiyang Xie E-mail:xiyangxie@ncepu.edu.cn
基金资助:
Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 2024MS126).

Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions

Luyao Zhang(张路瑶) and Xiyang Xie(解西阳)†

Department of Mathematics and Physics, Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China

Received:2024-06-27 Revised:2024-07-07 Accepted:2024-07-12 Online:2024-09-15 Published:2024-08-30
Contact: Xiyang Xie E-mail:xiyangxie@ncepu.edu.cn
Supported by:
Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 2024MS126).

摘要/Abstract

摘要： We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrödinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses on the dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions under non-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole or double-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and the spatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons, we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions. In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle” crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one and two dark solitons.

关键词: double-pole solitons, double-pole breathers, Riemann-Hilbert problem, non-zero boundary conditions, nonlinear Schrödinger equation with sextic operator

Abstract: We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrödinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses on the dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions under non-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole or double-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and the spatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons, we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions. In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle” crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one and two dark solitons.

Key words: double-pole solitons, double-pole breathers, Riemann-Hilbert problem, non-zero boundary conditions, nonlinear Schrödinger equation with sextic operator

中图分类号: (Integrable systems)

02.30.Ik

02.30.Rz (Integral equations) 42.81.Dp (Propagation, scattering, and losses; solitons)

Luyao Zhang(张路瑶) and Xiyang Xie(解西阳). Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions[J]. 中国物理B, 2024, 33(9): 90207-090207.

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Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions

Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions

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