On the matrix negative order Korteweg–de Vries equation — the commutative case

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2025-04-30 DOI:10.1016/j.wavemoti.2025.103562

T. Kriecherbauer , G.U. Urazboev , A.K. Babadjanova

引用次数: 0

Abstract

This work is devoted to the application of the inverse scattering transform method to the matrix negative order Korteweg–de Vries (mNKdV) equation in the commutative case. First, we obtain the time evolution of the scattering data for the corresponding matrix Sturm–Liouville operator with a self-adjoint potential. This then leads to a general construction procedure for solutions of the mNKdV equation that can also be used for solving initial value problems. We illustrate our results by presenting explicit formulas for arbitrary multi-soliton solutions in the reflectionless case.

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关于矩阵负阶Korteweg-de Vries方程-交换情况

本文研究了矩阵负阶Korteweg-de Vries （mNKdV）方程在交换情况下的逆散射变换方法的应用。首先，我们得到了具有自伴随势的相应矩阵Sturm-Liouville算子散射数据的时间演化。这就引出了mNKdV方程解的一般构造程序，该程序也可用于求解初值问题。我们通过给出无反射情况下任意多孤子解的显式公式来说明我们的结果。

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

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.