Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations

Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations

In this paper, by applying the Jacobian ellipse function method, we obtain a group of periodic traveling wave solution of coupled KdV equations. Furthermore, by the implicit function theorem, the relation between some wave velocity and the solution’s period is researched. Lastly, we show that this t...

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Main Author: Cong Sun
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2020/3875038
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spelling doaj-01ff73e0b6a445e4bfd40e2e09ae2bb92021-07-02T11:44:08ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/38750383875038Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV EquationsCong Sun0College of Applied Mathematics, Jilin University of Finance and Economics, Changchun, Jilin 130117, ChinaIn this paper, by applying the Jacobian ellipse function method, we obtain a group of periodic traveling wave solution of coupled KdV equations. Furthermore, by the implicit function theorem, the relation between some wave velocity and the solution’s period is researched. Lastly, we show that this type of solution is orbitally stable by periodic perturbations of the same wavelength as the underlying wave.http://dx.doi.org/10.1155/2020/3875038
collection DOAJ
language English
format Article
sources DOAJ
author Cong Sun
spellingShingle Cong Sun
Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations
Advances in Mathematical Physics
author_facet Cong Sun
author_sort Cong Sun
title Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations
title_short Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations
title_full Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations
title_fullStr Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations
title_full_unstemmed Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations
title_sort nonlinear stability of the periodic traveling wave solution for a class of coupled kdv equations
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2020-01-01
description In this paper, by applying the Jacobian ellipse function method, we obtain a group of periodic traveling wave solution of coupled KdV equations. Furthermore, by the implicit function theorem, the relation between some wave velocity and the solution’s period is researched. Lastly, we show that this type of solution is orbitally stable by periodic perturbations of the same wavelength as the underlying wave.
url http://dx.doi.org/10.1155/2020/3875038
work_keys_str_mv AT congsun nonlinearstabilityoftheperiodictravelingwavesolutionforaclassofcoupledkdvequations
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