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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/3875038 |
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| author | Cong Sun |
| author_facet | Cong Sun |
| author_sort | Cong Sun |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-01ff73e0b6a445e4bfd40e2e09ae2bb9 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-01ff73e0b6a445e4bfd40e2e09ae2bb92025-08-20T02:01:46ZengWileyAdvances 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 |
| spellingShingle | Cong Sun Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations Advances in Mathematical Physics |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2020/3875038 |
| work_keys_str_mv | AT congsun nonlinearstabilityoftheperiodictravelingwavesolutionforaclassofcoupledkdvequations |