SOLITARY WAVES OF SINGULARLY PERTURBED GENERALIZED KDV EQUATION WITH HIGH ORDER NONLINEARITY

被引：1
|
作者：
Wang, Jundong [1 ]
Zhang, Lijun [1 ,2 ]
Shchepakina, Elena [3 ]
Sobolev, Vladimir [3 ]
机构：
[1] Shandong Univ Sci & Technol, Dept Math, Qingdao 266590, Shandong, Peoples R China
[2] North West Univ, Int Inst Symmetry Anal & Math Modelling, Dept Math Sci, Mafikeng Campus, Mmabatho, South Africa
[3] Samara Natl Res Univ, Moskovskoye Shosse 34, Samara 443086, Russia
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2023年 / 16卷 / 3-4期
关键词：
Perturbed generalized KdV equation; solitary wave solution; dynamical system; geometric singular perturbation theory; Melnikov's method; PERIODIC-WAVES; TRAVELING-WAVES; EXISTENCE;
D O I：
10.3934/dcdss.2022124
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper is concerned on solitary waves for singularly perturbed generalized KdV equation with high order nonlinear terms. We firstly give the phase portraits of system related to the unperturbed equation under various cases by theory of planar dynamical system. Then by using geometric singular perturbation theory and Melnikov's method, the existence of solitary wave solutions of generalized KdV equations with high order nonlinear terms is established. It is proven that some solitary wave solutions with particular wave speeds will persist under small perturbations.
引用
收藏
页码：639 / 654
页数：16
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