Periodic and Solitary-Wave Solutions for a Variant of the K(3,2) Equation
We employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the K(3,2) equation. For the focusing branch, we obtain hump-shaped and valley-shaped solitary-wave solutions and som...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/582512 |
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| _version_ | 1832552498120884224 |
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| author | Jiangbo Zhou Lixin Tian |
| author_facet | Jiangbo Zhou Lixin Tian |
| author_sort | Jiangbo Zhou |
| collection | DOAJ |
| description | We employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the K(3,2) equation. For the focusing branch, we obtain hump-shaped and valley-shaped solitary-wave solutions and some periodic solutions. For the defocusing branch, the nonexistence of solitary traveling wave solutions is shown. Meanwhile, some periodic solutions are also obtained. The results presented in this paper supplement the previous results. |
| format | Article |
| id | doaj-art-4e5ea6f9e54f4ba3ac542424eaa0824f |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-4e5ea6f9e54f4ba3ac542424eaa0824f2025-02-03T05:58:28ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/582512582512Periodic and Solitary-Wave Solutions for a Variant of the K(3,2) EquationJiangbo Zhou0Lixin Tian1Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaNonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaWe employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the K(3,2) equation. For the focusing branch, we obtain hump-shaped and valley-shaped solitary-wave solutions and some periodic solutions. For the defocusing branch, the nonexistence of solitary traveling wave solutions is shown. Meanwhile, some periodic solutions are also obtained. The results presented in this paper supplement the previous results.http://dx.doi.org/10.1155/2011/582512 |
| spellingShingle | Jiangbo Zhou Lixin Tian Periodic and Solitary-Wave Solutions for a Variant of the K(3,2) Equation International Journal of Differential Equations |
| title | Periodic and Solitary-Wave Solutions for a Variant of the K(3,2)
Equation |
| title_full | Periodic and Solitary-Wave Solutions for a Variant of the K(3,2)
Equation |
| title_fullStr | Periodic and Solitary-Wave Solutions for a Variant of the K(3,2)
Equation |
| title_full_unstemmed | Periodic and Solitary-Wave Solutions for a Variant of the K(3,2)
Equation |
| title_short | Periodic and Solitary-Wave Solutions for a Variant of the K(3,2)
Equation |
| title_sort | periodic and solitary wave solutions for a variant of the k 3 2 equation |
| url | http://dx.doi.org/10.1155/2011/582512 |
| work_keys_str_mv | AT jiangbozhou periodicandsolitarywavesolutionsforavariantofthek32equation AT lixintian periodicandsolitarywavesolutionsforavariantofthek32equation |