Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations
We investigate the traveling wave solutions for the ZK-BBM() equations by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2) equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the pe...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/156139 |
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| author | Shaoyong Li Zhengrong Liu |
| author_facet | Shaoyong Li Zhengrong Liu |
| author_sort | Shaoyong Li |
| collection | DOAJ |
| description | We investigate the traveling wave solutions for the ZK-BBM() equations by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2) equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. Secondly, for ZK-BBM(3, 2) equation, we obtain some elliptic function solutions which include periodic blow-up and periodic wave. Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave. We also show that our work extends some previous results. |
| format | Article |
| id | doaj-art-04515c7b3951457192484b9050f26b36 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-04515c7b3951457192484b9050f26b362025-02-03T06:11:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/156139156139Some Further Results on Traveling Wave Solutions for the ZK-BBM() EquationsShaoyong Li0Zhengrong Liu1College of Mathematics and Information Sciences, Shaoguan University, Shaoguan, Guangdong 512005, ChinaDepartment of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, ChinaWe investigate the traveling wave solutions for the ZK-BBM() equations by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2) equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. Secondly, for ZK-BBM(3, 2) equation, we obtain some elliptic function solutions which include periodic blow-up and periodic wave. Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave. We also show that our work extends some previous results.http://dx.doi.org/10.1155/2013/156139 |
| spellingShingle | Shaoyong Li Zhengrong Liu Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations Journal of Applied Mathematics |
| title | Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations |
| title_full | Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations |
| title_fullStr | Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations |
| title_full_unstemmed | Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations |
| title_short | Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations |
| title_sort | some further results on traveling wave solutions for the zk bbm equations |
| url | http://dx.doi.org/10.1155/2013/156139 |
| work_keys_str_mv | AT shaoyongli somefurtherresultsontravelingwavesolutionsforthezkbbmequations AT zhengrongliu somefurtherresultsontravelingwavesolutionsforthezkbbmequations |