All exact traveling wave solutions of the combined KdV-mKdV equation
In this article, we employ the complex method to obtain all meromorphic solutions of complex combined Korteweg-de Vries-modified Korteweg-de Vries equation (KdV-mKdV equation) at first, then we find all exact traveling wave solutions of the combined KdV-mKdV equation. The idea introduced in this pap...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Springer Verlag
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/7341 |
| _version_ | 1848745341133783040 |
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| author | Huang, Y. Wu, Yong Hong Meng, F. Yuan, W. |
| author_facet | Huang, Y. Wu, Yong Hong Meng, F. Yuan, W. |
| author_sort | Huang, Y. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this article, we employ the complex method to obtain all meromorphic solutions of complex combined Korteweg-de Vries-modified Korteweg-de Vries equation (KdV-mKdV equation) at first, then we find all exact traveling wave solutions of the combined KdV-mKdV equation. The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic exact traveling wave solutions of the combined KdV-mKdV equation are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions wr,2(z)wr,2(z) and simply periodic solutions ws,2(z)ws,2(z) such that they are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role in finding exact solutions in mathematical physics. We also give some computer simulations to illustrate our main results. |
| first_indexed | 2025-11-14T06:15:49Z |
| format | Journal Article |
| id | curtin-20.500.11937-7341 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:15:49Z |
| publishDate | 2014 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-73412017-09-13T14:36:23Z All exact traveling wave solutions of the combined KdV-mKdV equation Huang, Y. Wu, Yong Hong Meng, F. Yuan, W. In this article, we employ the complex method to obtain all meromorphic solutions of complex combined Korteweg-de Vries-modified Korteweg-de Vries equation (KdV-mKdV equation) at first, then we find all exact traveling wave solutions of the combined KdV-mKdV equation. The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic exact traveling wave solutions of the combined KdV-mKdV equation are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions wr,2(z)wr,2(z) and simply periodic solutions ws,2(z)ws,2(z) such that they are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role in finding exact solutions in mathematical physics. We also give some computer simulations to illustrate our main results. 2014 Journal Article http://hdl.handle.net/20.500.11937/7341 10.1186/1687-1847-2014-261 Springer Verlag fulltext |
| spellingShingle | Huang, Y. Wu, Yong Hong Meng, F. Yuan, W. All exact traveling wave solutions of the combined KdV-mKdV equation |
| title | All exact traveling wave solutions of the combined KdV-mKdV equation |
| title_full | All exact traveling wave solutions of the combined KdV-mKdV equation |
| title_fullStr | All exact traveling wave solutions of the combined KdV-mKdV equation |
| title_full_unstemmed | All exact traveling wave solutions of the combined KdV-mKdV equation |
| title_short | All exact traveling wave solutions of the combined KdV-mKdV equation |
| title_sort | all exact traveling wave solutions of the combined kdv-mkdv equation |
| url | http://hdl.handle.net/20.500.11937/7341 |