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The extended hyperbolic functions method and new exact solutions to the Zakharov equations. (English) Zbl 1143.65083
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.

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