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A new rational auxiliary equation method and exact solutions of a generalized Zakharov system. (English) Zbl 1180.35445
Summary: A new rational auxiliary equation method for obtaining exact traveling wave solutions of constant coefficient nonlinear partial differential equations of evolution is proposed. Its effectiveness is evinced by obtaining exact solutions of a generalized Zakharov system, some of which are new. It is shown that the $G{}^{\text{'}}/G$ and the generalized projective Ricatti expansion methods are special cases of the auxiliary equation method. Further, due the solutions obtained, four other new and practicable rational methods are deduced.
##### MSC:
 35Q51 Soliton-like equations 35C07 Traveling wave solutions of PDE 35A24 Methods of ordinary differential equations for PDE 35A30 Geometric theory for PDE, characteristics, transformations
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