Existence of Solitary Wave Solutions for a Nonlinear Fifth-Order KdV Equation

被引：0
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作者：
Xiaofeng Li
Zengji Du
Jiang Liu
机构：
[1] Jiangsu Normal University,School of Mathematics and Statistics
[2] Xuzhou Vocational Technology Academy of Finance and Economics,Department of Mathematics
来源：
Qualitative Theory of Dynamical Systems | 2020年 / 19卷
关键词：
Fifth-order KdV equation; Homoclinic orbits; Solitary waves; Geometric singular perturbation; 35Q53; 34D15; 35C07;
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摘要：
In this paper, we study a nonlinear fifth-order KdV equation which has wide physical applications. We first establish the existence of solitary wave solutions for this equation without delay by using the Hamilton function method. Then we obtain the desired homoclinic orbits by constructing a locally invariant manifold. Finally we obtain the existence of solitary wave solutions for this equation with local and nonlocal delay convolution kernels by using the geometric singular perturbation analysis, implicit function theorem and Fredholm theory.
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