All traveling wave exact solutions of two kinds of nonlinear evolution equations
In this article, we employ the complex method to obtain all meromorphic solutions of complex Korteweg–de Vries (KdV) equation and the modified Benjamin–Bona–Mahony (mBBM) equation at first, then find out all traveling wave exact solutions of the Eqs. (KdV) and (mBBM). The idea introduced in this pap...
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Published: |
Elsevier Inc.
2014
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/19254 |
| _version_ | 1848749980164030464 |
|---|---|
| author | Huang, Y. Yuan, W. Wu, Yong Hong |
| author_facet | Huang, Y. Yuan, W. Wu, Yong Hong |
| 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 Korteweg–de Vries (KdV) equation and the modified Benjamin–Bona–Mahony (mBBM) equation at first, then find out all traveling wave exact solutions of the Eqs. (KdV) and (mBBM). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic solutions of the Eqs. (KdV) and (mBBM) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions w2r,2(z)w2r,2(z) and simply periodic solutions w2s,1(z)w2s,1(z) which are not only new but also not degenerated successively by the elliptic function solutions. We give some computer simulations to illustrate our main results. |
| first_indexed | 2025-11-14T07:29:33Z |
| format | Journal Article |
| id | curtin-20.500.11937-19254 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:29:33Z |
| publishDate | 2014 |
| publisher | Elsevier Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-192542017-09-13T13:43:51Z All traveling wave exact solutions of two kinds of nonlinear evolution equations Huang, Y. Yuan, W. Wu, Yong Hong Exact solution Meromorphic function Elliptic function The Korteweg–de Vries equation The modified Benjamin–Bona–Mahony equation In this article, we employ the complex method to obtain all meromorphic solutions of complex Korteweg–de Vries (KdV) equation and the modified Benjamin–Bona–Mahony (mBBM) equation at first, then find out all traveling wave exact solutions of the Eqs. (KdV) and (mBBM). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic solutions of the Eqs. (KdV) and (mBBM) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions w2r,2(z)w2r,2(z) and simply periodic solutions w2s,1(z)w2s,1(z) which are not only new but also not degenerated successively by the elliptic function solutions. We give some computer simulations to illustrate our main results. 2014 Journal Article http://hdl.handle.net/20.500.11937/19254 10.1016/j.amc.2014.02.071 Elsevier Inc. restricted |
| spellingShingle | Exact solution Meromorphic function Elliptic function The Korteweg–de Vries equation The modified Benjamin–Bona–Mahony equation Huang, Y. Yuan, W. Wu, Yong Hong All traveling wave exact solutions of two kinds of nonlinear evolution equations |
| title | All traveling wave exact solutions of two kinds of nonlinear evolution equations |
| title_full | All traveling wave exact solutions of two kinds of nonlinear evolution equations |
| title_fullStr | All traveling wave exact solutions of two kinds of nonlinear evolution equations |
| title_full_unstemmed | All traveling wave exact solutions of two kinds of nonlinear evolution equations |
| title_short | All traveling wave exact solutions of two kinds of nonlinear evolution equations |
| title_sort | all traveling wave exact solutions of two kinds of nonlinear evolution equations |
| topic | Exact solution Meromorphic function Elliptic function The Korteweg–de Vries equation The modified Benjamin–Bona–Mahony equation |
| url | http://hdl.handle.net/20.500.11937/19254 |