Existence and stability of traveling waves of the fifth-order KdV equation

被引：4
|
作者：
Esfahani, Amin [1 ]
Levandosky, Steven [2 ]
机构：
[1] Nazarbayev Univ, Dept Math, Nur Sultan 010000, Kazakhstan
[2] Coll Holy Cross, Math & Comp Sci Dept, Worcester, MA 01610 USA
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2021年 / 421卷
关键词：
KdV equation; Solitary Waves; Ground States; Stability; CONCENTRATION-COMPACTNESS PRINCIPLE; SOLITARY WAVES; MASLOV INDEX; WATER; INSTABILITY; CALCULUS; MODELS;
D O I：
10.1016/j.physd.2021.132872
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the existence and stability of traveling waves of the Fifth-Order KdV equation for a general class of nonlinearities that satisfy power-like scaling relations. This class of nonlinearities includes sums and differences of powers. For such nonlinearities we use variational methods to show that there exist ground state traveling wave solutions and use the variational properties of the ground states to analyze their stability. (C) 2021 Elsevier B.V. All rights reserved.
引用
收藏
页数：21
相关论文
共 50 条
  • [1] Modeling Solitary Waves of the Fifth-order KdV Equation
    Tao, Zhao-Ling
    Gui, Bing
    Yang, Yang
    Qiu, Ming-Fei
    PROCEEDINGS OF THE 2010 INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS AND PHYSICS, VOL 2: ADVANCES ON APPLIED MATHEMATICS AND COMPUTATION MATHEMATICS, 2010, : 228 - 231
  • [2] Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework
    Bridges, TJ
    Derks, G
    Gottwald, G
    PHYSICA D-NONLINEAR PHENOMENA, 2002, 172 (1-4) : 190 - 216
  • [3] Dispersive shock waves in the fifth-order modified KdV equation
    Jing, Dong-Rao
    Zhang, Hai-Qiang
    Wei, Nan-Nan
    APPLIED MATHEMATICS LETTERS, 2025, 163
  • [4] On the stability of solitary wave solutions of the fifth-order KdV equation
    Buryak, AV
    Champneys, AR
    PHYSICS LETTERS A, 1997, 233 (1-2) : 58 - 62
  • [5] On the stability of solitary wave solutions of the fifth-order KdV equation
    Buryak, A.V.
    Champneys, A.R.
    Physics Letters, Section A: General, Atomic and Solid State Physics, 1997, 233 (1-2): : 58 - 62
  • [6] Existence of Solitary Wave Solutions for a Nonlinear Fifth-Order KdV Equation
    Xiaofeng Li
    Zengji Du
    Jiang Liu
    Qualitative Theory of Dynamical Systems, 2020, 19
  • [7] Existence of Solitary Wave Solutions for a Nonlinear Fifth-Order KdV Equation
    Li, Xiaofeng
    Du, Zengji
    Liu, Jiang
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2020, 19 (01)
  • [8] Solitons in the Fifth-Order KdV Equation with a Perturbation
    Li, Wentao
    Chen, Yipu
    Zhang, Zhao
    Yang, Xiangyu
    Li, Biao
    CHINESE PHYSICS LETTERS, 2025, 42 (01)
  • [9] Computational method for the fifth-order KdV equation
    Zuo, Jin-Ming
    Zhang, Yao-Ming
    Zhang, Rui
    2010 SECOND ETP/IITA WORLD CONGRESS IN APPLIED COMPUTING, COMPUTER SCIENCE, AND COMPUTER ENGINEERING, 2010, : 20 - 23
  • [10] Localized waves solutions for the fifth-order coupled extended modified KdV equation
    Song, N.
    Liu, R.
    Guo, M. M.
    Ma, W. X.
    WAVE MOTION, 2024, 124
12345