The existence of solitary waves of singularly perturbed mKdV–KS equation
The existence of solitary waves of singularly perturbed mKdV–KS equation
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DOI：
10.1016/j.chaos.2005.02.014
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发表时间：
2005-11
影响因子：
7.8
通讯作者：
Xinghua Fan;L. Tian
中科院分区：
文献类型：
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作者：
Xinghua Fan;L. Tian
本文研究了一类非线性反应扩散方程，它是基于带有高阶奇异摄动项的修正Korteweg-de Vries （mKdV）方程，即Kuramoto-Sivashinsky （KS）方程，称为mKdV - KS方程。特别注意孤波解的存在性问题。基于孤波解与相关常微分方程的同斜轨道的类比，从几何奇异摄动的角度证明了当摄动参数适当小时孤波存在。这个论证不需要原始mKdV孤立波解的显式表达式。
We study a sort of nonlinear reaction diffusion equation based on the modified Korteweg–de Vries (mKdV) equation with a higher order singularly perturbing term as the Kuramoto–Sivashinsky (KS) equation, called mKdV–KS equation. Special attention is paid to the question of the existence of solitary wave solutions. Based on the analogue between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, from geometric singular perturbation point of view, we prove that solitary wave persists when the perturbation parameter is suitably small. This argument does not require an explicit expression for the original mKdV solitary wave solution.