On existence of kink and antikink wave solutions of singularly perturbed Gardner equation

被引：15
|
作者：
Wen, Zhenshu [1 ]
机构：
[1] Huaqiao Univ, Fujian Prov Univ Key Lab Computat Sci, Sch Math Sci, Quanzhou 362021, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2020年 / 43卷 / 07期
基金：
中国国家自然科学基金;
关键词：
geometric singular perturbation theory; kink and antikink waves; Melnikov function; singularly perturbed Gardner equation; SOLITARY; BIFURCATIONS; DYNAMICS;
D O I：
10.1002/mma.6204
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the existence of kink and antikink wave solutions of singularly perturbed Gardner equation from the geometric perspective. We obtain the sufficient conditions to guarantee the existence of kink and antikink wave solutions of the singularly perturbed Gardner equation when the perturbation parameter is sufficiently small, by exploiting the geometric singular perturbation theory and the Melnikov function method.
引用
收藏
页码：4422 / 4427
页数：6
相关论文
共 50 条
  • [1] Existence of Kink and Antikink Wave Solutions of Singularly Perturbed Modified Gardner Equation
    Yan, Weifang
    Wang, Linlin
    Zhang, Min
    MATHEMATICS, 2024, 12 (06)
  • [2] Persistence of solitary wave solutions of singularly perturbed Gardner equation
    Tang, Yaning
    Xu, Wei
    Shen, Jianwei
    Gao, Liang
    CHAOS SOLITONS & FRACTALS, 2008, 37 (02) : 532 - 538
  • [3] Existence of Traveling Wave Solutions for the Perturbed Modefied Gardner Equation
    Yao Qi
    Yu Tian
    Yuheng Jiang
    Qualitative Theory of Dynamical Systems, 2024, 23
  • [4] Existence of Traveling Wave Solutions for the Perturbed Modefied Gardner Equation
    Qi, Yao
    Tian, Yu
    Jiang, Yuheng
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2024, 23 (03)
  • [5] EXISTENCE OF THE PERTURBED SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATION IN THE SINGULARLY PERTURBED DOMAINS
    JIMBO, S
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1988, 64 (02) : 33 - 36
  • [6] EXISTENCE OF TRAVELING WAVE SOLUTIONS IN A SINGULARLY PERTURBED PREDATOR-PREY EQUATION WITH SPATIAL DIFFUSION
    Zhu, Zirui
    Liu, Xingbo
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2024, 44 (01) : 78 - 115
  • [7] New solitons and kink solutions for the Gardner equation
    Wazwaz, Abdul-Majid
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2007, 12 (08) : 1395 - 1404
  • [8] Solitary wave solution to a singularly perturbed generalized Gardner equation with nonlinear terms of any order
    J B ZHOU
    J XU
    J D WEI
    X Q YANG
    Pramana, 2017, 88
  • [9] Solitary wave solution to a singularly perturbed generalized Gardner equation with nonlinear terms of any order
    Zhou, J. B.
    Xu, J.
    Wei, J. D.
    Yang, X. Q.
    PRAMANA-JOURNAL OF PHYSICS, 2017, 88 (04):
  • [10] Mathematical studies on generalized Burgers Huxley equation and its singularly perturbed form: Existence of traveling wave solutions
    Zhang, Xiaohan
    Tian, Yu
    Zhang, Mingji
    Qi, Yao
    NONLINEAR DYNAMICS, 2025, 113 (03) : 2625 - 2634
12345