N $N$ -Soliton Matrix mKdV Solutions: Some Special Solutions Revisited

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-06-04 DOI:10.1111/sapm.70061

Sandra Carillo, Mauro Lo Schiavo, Cornelia Schiebold

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引用次数: 0

Abstract

In this article, a general solution formula is derived for the $d \times d$ -matrix modified Korteweg–de Vries equation. Then, a solution class corresponding to special parameter choices is examined in detail. Roughly, this class can be described as $N$ -solitons (in the sense of Goncharenko) with common phase matrix. It turns out that such a solution even takes values in a commutative subalgebra of the $d \times d$ -matrices. We arrive at a rich picture of possibilities for generalized 1-solitons and at visual patterns of $N$ -solitons which combine nonlinear with linear features. The impact of the phase matrix is visualized in computer plots.

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N$ N$ -孤子矩阵mKdV解：一些特殊解的再探讨

本文导出了d × d ${\sf d}\乘以{\sf d}$ -矩阵修正Korteweg-de Vries方程的通解公式。然后，详细分析了特殊参数选择对应的解类。粗略地说，这类可以被描述为具有共同相位矩阵的N$ N$ -孤子（在Goncharenko的意义上）。结果证明，这样的解甚至取d × d ${\sf d}\乘以{\sf d}$ -矩阵的交换子代数中的值。我们得到了广义1-孤子的丰富的可能性图景，以及结合了非线性和线性特征的N$ N$ -孤子的视觉模式。相矩阵的影响在计算机图中可视化。

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

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.