Dispersive shock waves in the fifth-order modified KdV equation

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-01-22 DOI:10.1016/j.aml.2025.109468

Dong-Rao Jing, Hai-Qiang Zhang, Nan-Nan Wei

引用次数: 0

Abstract

This study focuses on the Whitham modulation theory of the fifth-order modified KdV equation (5mKdV), successfully deriving the solutions for modulated periodic waves and establishing corresponding Whitham equations. Through the detailed analysis of the initial step solution, the rarefaction waves and two types of dispersive shock wave structures are revealed. Our results not only enrich the theoretical system of the 5mKdV equation but also provide valuable theoretical support for the analysis and control of wave phenomena.

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五阶修正KdV方程中的色散激波

本文研究了五阶修正KdV方程（5mKdV）的Whitham调制理论，成功地推导了调制周期波的解，并建立了相应的Whitham方程。通过对初始阶跃解的详细分析，揭示了稀疏波和两种类型的色散激波结构。我们的研究结果不仅丰富了5mKdV方程的理论体系，而且为波动现象的分析和控制提供了有价值的理论支持。

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

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.