Existence of Solitary Waves in a Perturbed KdV-mKdV Equation
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 homocl...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2270924 |
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| _version_ | 1849308505596493824 |
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| author | Chengqun Li Minzhi Wei Yuanhua Lin |
| author_facet | Chengqun Li Minzhi Wei Yuanhua Lin |
| author_sort | Chengqun Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-154414e01b3241aa8c1dd709b08222af |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-154414e01b3241aa8c1dd709b08222af2025-08-20T03:54:25ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/22709242270924Existence of Solitary Waves in a Perturbed KdV-mKdV EquationChengqun Li0Minzhi Wei1Yuanhua Lin2Deparment of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, ChinaDeparment of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, ChinaSchool of Mathematics and Statistics, Hechi University, Yizhou, Hechi, Guangxi 546300, ChinaIn 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.http://dx.doi.org/10.1155/2021/2270924 |
| spellingShingle | Chengqun Li Minzhi Wei Yuanhua Lin Existence of Solitary Waves in a Perturbed KdV-mKdV Equation Journal of Mathematics |
| title | Existence of Solitary Waves in a Perturbed KdV-mKdV Equation |
| title_full | Existence of Solitary Waves in a Perturbed KdV-mKdV Equation |
| title_fullStr | Existence of Solitary Waves in a Perturbed KdV-mKdV Equation |
| title_full_unstemmed | Existence of Solitary Waves in a Perturbed KdV-mKdV Equation |
| title_short | Existence of Solitary Waves in a Perturbed KdV-mKdV Equation |
| title_sort | existence of solitary waves in a perturbed kdv mkdv equation |
| url | http://dx.doi.org/10.1155/2021/2270924 |
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