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Extended \(F\)-expansion method and periodic wave solutions for the generalized Zakharov equations. (English) Zbl 1181.35255
Summary: We present an extended \(F\)-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the extended \(F\)-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously a number of periodic wave solutions expressed by various Jacobi elliptic functions for the generalized Zakharov equations. In the limit cases, the solitary wave solutions are obtained as well.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
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