n 分量广义高阶萨萨-萨妻方程的 N 索利子解的相互作用和渐近分析。

IF 2.7 2区数学 Q1 MATHEMATICS, APPLIED

Chaos Pub Date : 2024-12-01 DOI:10.1063/5.0237425

Zhuojie Lin, Zhenya Yan

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引用次数: 0

摘要

本文系统地研究了可积分的 n 分量三阶-五阶 Sasa-Satsuma 方程的 N-孑子和渐近分析。我们对（n+2）阶矩阵拉克斯对进行谱分析，提出黎曼-希尔伯特（RH）问题，并通过行列式生成 N-孑子解。此外，我们还直观地表示了多孑子解的相互作用动力学，并分析了它们的渐近行为。最后，我们通过处理具有高阶零点的 RH 问题，提出了高阶 N-soliton 解。这些结果将有助于进一步分析多孑子结构和设计相关的物理实验。

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Interactions and asymptotic analysis of N-soliton solutions for the n-component generalized higher-order Sasa-Satsuma equations.

In this paper, we systematically study the N-solitons and asymptotic analysis of the integrable n-component third-fifth-order Sasa-Satsuma equations. We conduct the spectral analysis on the (n+2)-order matrix Lax pair to formulate a Riemann-Hilbert (RH) problem, which is used to generate the N-soliton solutions via the determinants. Moreover, we visually represent the interaction dynamics of multi-soliton solutions and analyze their asymptotic behaviors. Finally, we present the higher-order N-soliton solutions by dealing with the RH problem with higher-order zeros. These results will be useful to further analyze the multi-soliton structures and design the related physical experiments.

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来源期刊

Chaos 物理-物理：数学物理

CiteScore

5.20

自引率

13.80%

发文量

448

审稿时长

2.3 months

期刊介绍： Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.