The Cauchy matrix structure and solutions of the three-component mKdV equations

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-02-01 DOI:10.1016/j.cnsns.2024.108456

Mengli Tian , Chunxia Li , Yehui Huang , Yuqin Yao

引用次数: 0

Abstract

Starting from a 4 × 4 matrix Sylvester equation, the matrix mKdV system as an unreduced equation is worked out and the explicit expression of its solution is presented by applying the Cauchy matrix method. Then, two kinds of reduction conditions are given, under which the complex three-component mKdV(CTC-mKdV) equation and the real three-component mKdV(RTC-mKdV) equation can be obtained, and finally, the explicit expressions of soliton solution and Jordan block solution for CTC-mKdV equation and RTC-mKdV equation are presented, respectively. Specially, the generated conditions of one-soliton solutions, two-soliton solutions, double-pole solutions, symmetry broken solutions and soliton molecule are presented, and their dynamic behaviors were analyzed.

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从 4 × 4 矩阵西尔维斯特方程出发，运用考奇矩阵法计算出未还原方程的矩阵 mKdV 系统，并给出其解的显式表达。然后，给出了两种还原条件，在这两种条件下可以得到复三元 mKdV（CTC-mKdV）方程和实三元 mKdV（RTC-mKdV）方程，最后分别给出了 CTC-mKdV 方程和 RTC-mKdV 方程的孤子解和约旦块解的显式。特别是给出了单孤子解、双孤子解、双极解、对称破缺解和孤子分子的生成条件，并分析了它们的动力学行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.