Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

doi:10.1088/1674-1056/ad4d64

中国物理B ›› 2024, Vol. 33 ›› Issue (8): 80201-080201.doi: 10.1088/1674-1056/ad4d64

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Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

Hui-Chao Zhao(赵会超), Lei-Nuo Ma(马雷诺), and Xi-Yang Xie(解西阳)†

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

收稿日期:2024-04-16 修回日期:2024-05-15 出版日期:2024-08-15 发布日期:2024-07-30
通讯作者: Xi-Yang Xie E-mail:xiyangxie@ncepu.edu.cn
基金资助:
Project supported by the Natural Science Foundation of Hebei Province, China (Grant No. A2021502004) and the Fundamental Research Funds for the Central Universities (Grant No. 2024MS126).

Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

Hui-Chao Zhao(赵会超), Lei-Nuo Ma(马雷诺), and Xi-Yang Xie(解西阳)†

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

Received:2024-04-16 Revised:2024-05-15 Online:2024-08-15 Published:2024-07-30
Contact: Xi-Yang Xie E-mail:xiyangxie@ncepu.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Hebei Province, China (Grant No. A2021502004) and the Fundamental Research Funds for the Central Universities (Grant No. 2024MS126).

摘要/Abstract

摘要： This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions. These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers. By analyzing the Lax pair and the Riemann-Hilbert problem, we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system. Furthermore, we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors. Through appropriate parameter selections, we observe various nonlinear phenomena, including the disappearance of solitons after interaction and their transformation into breather-like solitons, as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.

关键词: soliton, Riemann-Hilbert problem, non-zero boundary conditions, coupled Lakshmanan-Porsezian-Daniel equation

Abstract: This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions. These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers. By analyzing the Lax pair and the Riemann-Hilbert problem, we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system. Furthermore, we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors. Through appropriate parameter selections, we observe various nonlinear phenomena, including the disappearance of solitons after interaction and their transformation into breather-like solitons, as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.

Key words: soliton, Riemann-Hilbert problem, non-zero boundary conditions, coupled Lakshmanan-Porsezian-Daniel equation

中图分类号: (Integral equations)

02.30.Rz

02.30.Ik (Integrable systems) 05.45.Yv (Solitons)

Hui-Chao Zhao(赵会超), Lei-Nuo Ma(马雷诺), and Xi-Yang Xie(解西阳). Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions[J]. 中国物理B, 2024, 33(8): 80201-080201.

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Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

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