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

Li, Xiaofeng; Du, Zhijiang; Liu, Jiang

doi:10.1007/s12346-020-00366-5

Cited by 5 publications

(1 citation statement)

References 19 publications

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“…More recently, Ji and Li [15] considered the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system and the geometric singular perturbation theory. Besides, there are many literatures are the relevant applications on geometric singular perturbation theory, see [16,17,18,19,20,21,22]. More precisely, Zeng, Sun and Yu [23] considered the system (1.1) with D(u) = 1, F (u) = a 0 +2a 1 u, R(u) = u(u 2 −1)(u 2 +β).…”

Section: Introductionmentioning

confidence: 99%

Existence of traveling wave front for a generalized reaction-convection-diffusion equation

Wei

Dai

2022

Preprint

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In presented paper, the existence of traveling wave front for a generalized reaction-convection-diffusion equation with different delay convolution kernels is investigated by using the geometric singular perturbation theory. Firstly, we shall show that such traveling wave front exists without delay by qualitative analysis. After that, for the generalized reaction-convection-diffusion equation with a special local strong delay convolution kernel, the desired heteroclinic orbit is obtained by constructing a locally invariant manifold. Finally, with a nonlocal weak generic delay, the existence of traveling wave front is proved by implicit function theorem and Fredholm theory.

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