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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 \(G'/G\) and the generalized projective Riccati 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 equations |

35C07 | Traveling wave solutions |

35A24 | Methods of ordinary differential equations applied to PDEs |

35A30 | Geometric theory, characteristics, transformations in context of PDEs |

### Keywords:

rational auxiliary equation method; exact traveling wave solution; generalized Zakharov system
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\textit{O. P. Layeni}, Appl. Math. Comput. 215, No. 8, 2901--2907 (2009; Zbl 1180.35445)

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### References:

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