All traveling wave exact solutions of three kinds of nonlinear evolution equations
In this article, we employ the complex method to obtain all meromorphic exact solutions of complex Klein–Gordon (KG) equation, modified Korteweg-de Vries (mKdV) equation, and the generalized Boussinesq (gB) equation at first, then find all exact solutions of the Equations KG, mKdV, and gB. The idea...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
John Wiley & Sons Ltd.
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/18322 |
| _version_ | 1848749711336407040 |
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| author | Meng, F. Zhang, L. Wu, Yong Hong Yuan, W. |
| author_facet | Meng, F. Zhang, L. Wu, Yong Hong Yuan, W. |
| author_sort | Meng, F. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this article, we employ the complex method to obtain all meromorphic exact solutions of complex Klein–Gordon (KG) equation, modified Korteweg-de Vries (mKdV) equation, and the generalized Boussinesq (gB) equation at first, then find all exact solutions of the Equations KG, mKdV, and gB. The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic solutions are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions w2r,2.z/ and simply periodic solutions w1s,2.z/,w2s,1.z/ in these equations such that they are not only new but also not degenerated successively by the elliptic function solutions. We have also given some computer simulations to illustrate our main results. |
| first_indexed | 2025-11-14T07:25:17Z |
| format | Journal Article |
| id | curtin-20.500.11937-18322 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:25:17Z |
| publishDate | 2015 |
| publisher | John Wiley & Sons Ltd. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-183222017-01-30T12:07:09Z All traveling wave exact solutions of three kinds of nonlinear evolution equations Meng, F. Zhang, L. Wu, Yong Hong Yuan, W. In this article, we employ the complex method to obtain all meromorphic exact solutions of complex Klein–Gordon (KG) equation, modified Korteweg-de Vries (mKdV) equation, and the generalized Boussinesq (gB) equation at first, then find all exact solutions of the Equations KG, mKdV, and gB. The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic solutions are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions w2r,2.z/ and simply periodic solutions w1s,2.z/,w2s,1.z/ in these equations such that they are not only new but also not degenerated successively by the elliptic function solutions. We have also given some computer simulations to illustrate our main results. 2015 Journal Article http://hdl.handle.net/20.500.11937/18322 John Wiley & Sons Ltd. restricted |
| spellingShingle | Meng, F. Zhang, L. Wu, Yong Hong Yuan, W. All traveling wave exact solutions of three kinds of nonlinear evolution equations |
| title | All traveling wave exact solutions of three kinds of nonlinear evolution equations |
| title_full | All traveling wave exact solutions of three kinds of nonlinear evolution equations |
| title_fullStr | All traveling wave exact solutions of three kinds of nonlinear evolution equations |
| title_full_unstemmed | All traveling wave exact solutions of three kinds of nonlinear evolution equations |
| title_short | All traveling wave exact solutions of three kinds of nonlinear evolution equations |
| title_sort | all traveling wave exact solutions of three kinds of nonlinear evolution equations |
| url | http://hdl.handle.net/20.500.11937/18322 |