Dispersive shock waves in the fifth-order modified KdV equation

被引：0
|
作者：
Jing, Dong-Rao [1 ]
Zhang, Hai-Qiang [1 ]
Wei, Nan-Nan [1 ]
机构：
[1] Univ Shanghai Sci & Technol, Coll Sci, POB 253, Shanghai 200093, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2025年 / 163卷
关键词：
Fifth-order modified KdV equation; Periodic solutions; Whitham modulation theory; Riemann problem; NONLINEAR EVOLUTION-EQUATIONS;
D O I：
10.1016/j.aml.2025.109468
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页数：6
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