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New exact travelling wave solutions of bidirectional wave equations
Jonu Lee Rathinasamy Sakthivel
Volume 76 Issue 6 June 2011 pp 819-829
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https://www.ias.ac.in/article/fulltext/pram/076/06/0819-0829 -
Keywords
Travelling wave solutions ;tanh–coth function method ;Riccati equations ;symbolic computation. -
Abstract
The surface water waves in a water tunnel can be described by systems of the form [Bona and Chen, Physica D116, 191 (1998)] \begin{equation*}\begin{cases} v_t + u_x + (uv)_x + au_{x x x} − bv_{x x t} = 0,\\ u_t + v_x + u u_x + cv_{x x x} − d u_{x x t} = 0,\end{cases} \tag{1}\end{equation*} where 𝑎, 𝑏, 𝑐 and d are real constants. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution systems. In this paper, we obtain exact travelling wave solutions of system (1) using the modified tanh–coth function method with computerized symbolic computation.
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Author Affiliations
Jonu Lee1 Rathinasamy Sakthivel1
- Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
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Dates
- Published
- June 2011
- Manuscript received
- 18 November 2010
- Accepted
- 13 January 2011
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Pramana – Journal of Physics
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