|
| The Exact Solutions for the Benjamin-Bona-Mahony Equation |
| |
| View Full Text View/Add Comment Download reader |
| KeyWord:Generalized hyperbolic tangent function method The modified hyperbolic function expanding method Traveling wave solution Balance coefficient method Partial differential equation |
| Author Name | Affiliation | | Xiaofang Duan | School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710126, China | | Junliang Lu | School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China | | Yaping Ren | School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China | | Rui Ma | School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China |
|
| Hits: 280 |
| Download times: 400 |
| Abstract: |
| The Benjamin-Bona-Mahony (BBM) equation represents the unidirectional
propagation of nonlinear dispersive long waves, which has a clear
physical background, and is a more suitable mathematical and
physical equation than the KdV equation. Therefore, the research
on the BBM equation is very important. In this article, we put
forward an effective algorithm, the modified hyperbolic function
expanding method, to build the solutions of the BBM equation. We, by
utilizing the modified hyperbolic function expanding method,
obtain the traveling wave solutions of the BBM equation.
When the parameters are taken as special values, the solitary
waves are also derived from the traveling waves. The traveling
wave solutions are expressed by the hyperbolic functions, the
trigonometric functions and the rational functions. The modified
hyperbolic function expanding method is direct, concise, elementary
and effective, and can be used for many other nonlinear partial
differential equations. |
|
|
|
