Large ordinary differential equation systems and software

1982 ◽  
Vol 2 (4) ◽  
pp. 24-30 ◽  
Author(s):  
A. Hindmarsh
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Ordinary Differential Equation Systems

scholarly journals Existence of Solitary Waves in a Perturbed KdV-mKdV Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Chengqun Li ◽  
Minzhi Wei ◽  
Yuanhua Lin
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Solitary Wave ◽  
Perturbation Technique ◽  
Mkdv Equation ◽  
Slow Manifold ◽  
Melnikov Function ◽  
Homoclinic Loop ◽  
Singular Perturbation Technique ◽  
Ordinary Differential Equation Systems

In this paper, we establish the existence of a solitary wave in a KdV-mKdV equation with dissipative perturbation by applying the geometric singular perturbation technique and Melnikov function. The distance of the stable manifold and unstable manifold is computed to show the existence of the homoclinic loop for the related ordinary differential equation systems on the slow manifold, which implies the existence of a solitary wave for the KdV-mKdV equation with dissipative perturbation.

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