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Zbl 1143.65083
Shang, Yadong; Huang, Yong; Yuan, Wenjun
The extended hyperbolic functions method and new exact solutions to the Zakharov equations. (English)
[J] Appl. Math. Comput. 200, No. 1, 110-122 (2008). ISSN 0096-3003

Summary: The multiple exact solutions for the nonlinear evolution equations describing the interaction of laser-plasma are developed. The extended hyperbolic function method are employed to reveal these new solutions. The solutions include that of the solitary wave solutions of bell-type for $n$ and $E$, the solitary wave solutions of kink-type for $E$ and bell-type for $n$, the solitary wave solutions of a compound of the bell-type and the kink-type for $n$ and $E$, the singular traveling wave solutions, periodic traveling wave solutions of triangle function types, and solitary wave solutions of rational function types. In addition to re-deriving all known solutions in a systematic way, several new and more general solutions can be obtained by using our method.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35Q53 KdV-like equations

Keywords: explicit and exact solutions; solitary wave solutions; periodic wave solutions

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Zentralblatt MATH Berlin [Germany]