Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation
We use bifurcation method of dynamical systems to study exact traveling wave solutions of a nonlinear evolution equation. We obtain exact explicit expressions of bell-shaped solitary wave solutions involving more free parameters, and some existing results are corrected and improved. Also, we get som...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/943167 |
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| _version_ | 1832567829405106176 |
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| author | Zhengyong Ouyang |
| author_facet | Zhengyong Ouyang |
| author_sort | Zhengyong Ouyang |
| collection | DOAJ |
| description | We use bifurcation method of dynamical systems to study exact traveling wave solutions of a nonlinear evolution equation. We obtain exact explicit expressions of bell-shaped solitary wave solutions involving more free parameters, and some existing results are corrected and improved. Also, we get some new exact periodic wave solutions in parameter forms of the Jacobian elliptic function. Further, we find that the bell-shaped waves are limits of the periodic waves in some sense. The results imply that we can deduce bell-shaped waves from periodic waves for some nonlinear evolution equations. |
| format | Article |
| id | doaj-art-c9b324abaf794fe7acb9c2d8dd5c171e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c9b324abaf794fe7acb9c2d8dd5c171e2025-02-03T01:00:35ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/943167943167Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony EquationZhengyong Ouyang0Department of Mathematics, Foshan University, Foshan, Guangdong 528000, ChinaWe use bifurcation method of dynamical systems to study exact traveling wave solutions of a nonlinear evolution equation. We obtain exact explicit expressions of bell-shaped solitary wave solutions involving more free parameters, and some existing results are corrected and improved. Also, we get some new exact periodic wave solutions in parameter forms of the Jacobian elliptic function. Further, we find that the bell-shaped waves are limits of the periodic waves in some sense. The results imply that we can deduce bell-shaped waves from periodic waves for some nonlinear evolution equations.http://dx.doi.org/10.1155/2014/943167 |
| spellingShingle | Zhengyong Ouyang Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation Abstract and Applied Analysis |
| title | Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation |
| title_full | Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation |
| title_fullStr | Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation |
| title_full_unstemmed | Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation |
| title_short | Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation |
| title_sort | traveling wave solutions of the kadomtsev petviashvili benjamin bona mahony equation |
| url | http://dx.doi.org/10.1155/2014/943167 |
| work_keys_str_mv | AT zhengyongouyang travelingwavesolutionsofthekadomtsevpetviashvilibenjaminbonamahonyequation |