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Zbl 1039.65071
Khater, A. H.; Malfliet, W.; Kamel, E. S.
Travelling wave solutions of some classes of nonlinear evolution equations in $(1+1)$ and higher dimensions. (English)
[J] Math. Comput. Simul. 64, No. 2, 247-258 (2004). ISSN 0378-4754

Summary: 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.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
35K55 Nonlinear parabolic equations
35L70 Second order nonlinear hyperbolic equations
35Q53 KdV-like equations

Keywords: tanh method; wave equations; Korteweg-de Vries equations; Liouville's equation; stability; traveling wave solutions; tanh series solution method; nonlinear evolution equations; solitary waves;

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