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New exact travelling wave solutions of bidirectional wave equations

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Abstract

The surface water waves in a water tunnel can be described by systems of the form [Bona and Chen, Physica D116, 191 (1998)]

$$ \label{BWE} \left\{ \begin{array}{l} v_t+u_x+(uv)_x+au_{xxx}-bv_{xxt}=0, \\ u_t+v_x+uu_x+cv_{xxx}-du_{xxt}=0, \end{array} \right. $$
(1)

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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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Republic of Korea

    JONU LEE & RATHINASAMY SAKTHIVEL

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  1. JONU LEE
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  2. RATHINASAMY SAKTHIVEL
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Correspondence to RATHINASAMY SAKTHIVEL.

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LEE, J., SAKTHIVEL, R. New exact travelling wave solutions of bidirectional wave equations. Pramana - J Phys 76, 819–829 (2011). https://doi.org/10.1007/s12043-011-0105-4

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