Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation
Using an improved qualitative method which combines characteristics of several methods, we classify all travelling wave solutions of the modified Degasperis-Procesi equation in specified regions of the parametric space. Besides some popular exotic solutions including peaked waves, and looped and cus...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/548920 |
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| _version_ | 1832547130358628352 |
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| author | Jiuli Yin Liuwei Zhao Shanyu Ding |
| author_facet | Jiuli Yin Liuwei Zhao Shanyu Ding |
| author_sort | Jiuli Yin |
| collection | DOAJ |
| description | Using an improved qualitative method which combines characteristics of several methods, we classify all travelling wave solutions of the modified Degasperis-Procesi equation in specified regions of the parametric space. Besides some popular exotic solutions including peaked waves, and looped and cusped waves, this equation also admits some very particular waves, such as fractal-like waves, double stumpons, double kinked waves, and butterfly-like waves. The last three types of solutions have not been reported in the literature. Furthermore, we give the limiting behavior of all periodic solutions as the parameters trend to some special values. |
| format | Article |
| id | doaj-art-1527f3cc3a0f46f2abfe8ddab3eaad87 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-1527f3cc3a0f46f2abfe8ddab3eaad872025-02-03T06:45:56ZengWileyAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/548920548920Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi EquationJiuli Yin0Liuwei Zhao1Shanyu Ding2Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaNonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaNonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaUsing an improved qualitative method which combines characteristics of several methods, we classify all travelling wave solutions of the modified Degasperis-Procesi equation in specified regions of the parametric space. Besides some popular exotic solutions including peaked waves, and looped and cusped waves, this equation also admits some very particular waves, such as fractal-like waves, double stumpons, double kinked waves, and butterfly-like waves. The last three types of solutions have not been reported in the literature. Furthermore, we give the limiting behavior of all periodic solutions as the parameters trend to some special values.http://dx.doi.org/10.1155/2014/548920 |
| spellingShingle | Jiuli Yin Liuwei Zhao Shanyu Ding Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation Advances in Mathematical Physics |
| title | Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation |
| title_full | Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation |
| title_fullStr | Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation |
| title_full_unstemmed | Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation |
| title_short | Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation |
| title_sort | limiting behavior of travelling waves for the modified degasperis procesi equation |
| url | http://dx.doi.org/10.1155/2014/548920 |
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