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.
引用
收藏
页数：6
相关论文
共 50 条
  • [21] Higher-order rational soliton solutions for the fifth-order modified KdV and KdV equations
    Pei, Zhi-Jie
    Zhang, Hai-Qiang
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2021, 35 (03):
  • [22] LONG-TIME BEHAVIOR OF SOLUTIONS TO THE FIFTH-ORDER MODIFIED KDV-TYPE EQUATION
    Okamoto, Mamoru
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2018, 23 (9-10) : 751 - 792
  • [23] Higher-Order Rogue Waves for a Fifth-Order Dispersive Nonlinear Schrodinger Equation in an Optical Fibre
    Wang, Qi-Min
    Gao, Yi-Tian
    Su, Chuan-Qi
    Shen, Yu-Jia
    Feng, Yu-Jie
    Xue, Long
    ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2015, 70 (05): : 365 - 374
  • [24] Global dynamics of the generalized fifth-order KdV equation with quintic nonlinearity
    Yuexun Wang
    Journal of Evolution Equations, 2021, 21 : 1449 - 1475
  • [25] Soliton solutions for the fifth-order KdV equation with the homotopy analysis method
    S. Abbasbandy
    F. Samadian Zakaria
    Nonlinear Dynamics, 2008, 51 : 83 - 87
  • [26] Soliton solutions for the fifth-order KdV equation with the homotopy analysis method
    Abbasbandy, S.
    Zakaria, F. Samadian
    NONLINEAR DYNAMICS, 2008, 51 (1-2) : 83 - 87
  • [27] Global dynamics of the generalized fifth-order KdV equation with quintic nonlinearity
    Wang, Yuexun
    JOURNAL OF EVOLUTION EQUATIONS, 2021, 21 (02) : 1449 - 1475
  • [28] Multi-symplectic method for generalized fifth-order KdV equation
    Hu Wei-Peng
    Deng Zi-Chen
    CHINESE PHYSICS B, 2008, 17 (11) : 3923 - 3929
  • [29] Variants of the generalized fifth-order KdV equation with compact and noncompact structures
    Wazwaz, AM
    Helal, MA
    CHAOS SOLITONS & FRACTALS, 2004, 21 (03) : 579 - 589
  • [30] Nonlinear self-adjointness of a generalized fifth-order KdV equation
    Freire, Igor Leite
    Santos Sampaio, Julio Cesar
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (03)
12345