广义复数 mKdV 方程的 N 索利子解及其动态分析

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS Wave Motion Pub Date : 2024-05-15 DOI:10.1016/j.wavemoti.2024.103350
Xinshan Li , Ting Su , Jingru Geng
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引用次数: 0

摘要

利用黎曼-希尔伯特方法研究了一个新的广义复数修正科特韦格-德弗里斯(mKdV)方程。首先,我们为广义复数 mKdV 方程推导出一个与 3 × 3 矩阵谱问题相关的 Lax 对。然后,我们可以通过 Lax 对 x 部分的谱分析来提出黎曼-希尔伯特问题。根据势矩阵的对称性,我们可以找到黎曼-希尔伯特问题的两种零结构情况。通过求解特殊的黎曼-希尔伯特问题并利用反散射变换,我们得到了广义复 mKdV 方程的 N 索利子解的统一公式。此外,还通过选择适当的参数分析了单孑子解和双孑子解的动力学行为。
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N-soliton solutions and their dynamic analysis to the generalized complex mKdV equation

A new generalized complex modified Korteweg–de Vries (mKdV) equation is studied by using Riemann-Hilbert approach. Firstly, we derive a Lax pair associated with a 3 × 3 matrix spectral problem for the generalized complex mKdV equation. Then, we can formulate the Riemann-Hilbert problem via the spectral analysis of the x-part of the Lax pair. According to the symmetry properties of the potential matrix, we find two cases of zero structures for the Riemann-Hilbert problem. By solving the particular Riemann-Hilbert problem and using the inverse scattering transformation, we obtain the unified formulas of the N-soliton solutions for the generalized complex mKdV equation. In addition, the dynamical behaviors of the single-soliton solution and the two-soliton solution are analyzed by choosing appropriate parameters.

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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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