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Travelling wave solutions of some classes of nonlinear evolution equations in (1+1) and higher dimensions

Author

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  • Khater, A.H.
  • Malfliet, W.
  • Kamel, E.S.

Abstract

The tanh method is used to find travelling wave solutions to various wave equations. In particular, it is extended to solve a coupled set of (1+1) dimensional Korteweg–de Vries type of equations, (3+1) dimensional Korteweg–de Vries like equation and Liouville’s equation. Also the stability of those solutions is investigated.

Suggested Citation

  • Khater, A.H. & Malfliet, W. & Kamel, E.S., 2004. "Travelling wave solutions of some classes of nonlinear evolution equations in (1+1) and higher dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 247-258.
    • Handle: RePEc:eee:matcom:v:64:y:2004:i:2:p:247-258
    DOI: 10.1016/j.matcom.2003.09.024
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    References listed on IDEAS

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    1. Hereman, Willy & Nuseir, Ameina, 1997. "Symbolic methods to construct exact solutions of nonlinear partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(1), pages 13-27.
    2. Malfliet, W., 2003. "Travelling-wave solutions of coupled nonlinear evolution equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 101-108.
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    Cited by:

    1. Khater, A.H. & Hassan, M.M. & Temsah, R.S., 2005. "Cnoidal wave solutions for a class of fifth-order KdV equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(4), pages 221-226.

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