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New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations. (English) Zbl 1107.65094
Summary: The Kuramoto-Sivashinsky equation and the Kawahara equation are studied. The tanh method and the extended tanh method are used for analytic treatment for these two equations. By means of these methods, new solitary wave solutions are determined for each equation. The two approaches are reliable and manageable.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
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