Kundu-Eckhaus方程暗孤子的存在性

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 Epub Date: 2025-01-07 DOI:10.1016/j.physd.2025.134522

Ling Pan, Shihui Zhu

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引用次数: 0

摘要

本文分别讨论了无强泛延迟和具有强泛延迟的Kundu-Eckhaus方程的暗孤子解和周期孤波解。首先，在动力学系统参数方面，通过沿不同轨道积分得到了无延迟Kundu-Eckhaus方程的新的暗孤子和周期孤波解。然后，研究了Kundu-Eckhaus方程解的极限和调制稳定性。最后，利用几何奇异摄动理论证明了具有强一般时滞的Kundu-Eckhaus方程的两个暗孤子和两个周期孤子波解的存在性。

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Existence of dark solitons for Kundu–Eckhaus equations

This paper focuses on dark solitons and periodic solitary wave solutions for Kundu–Eckhaus equations without and with a strong generic delay, respectively. First, in terms of the dynamic system arguments, new dark solitons and periodic solitary wave solutions for the Kundu–Eckhaus equation without delay are obtained by integrating along different orbits. Then, the limits and modulation stability of the solutions of the Kundu–Eckhaus equation are investigated. Finally, the existence of two dark solitons and two periodic solitary wave solutions for Kundu–Eckhaus equations with a strong generic delays is proven via geometric singular perturbation theory.

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.