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A generalized new auxiliary equation method and its applications to nonlinear partial differential equations. (English) Zbl 1197.35008
Summary: A generalized new auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the combined KdV-mKdV equation and the \((2+1)\)-dimensional asymmetric Nizhnik-Novikov-Vesselov equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained.

MSC:
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
Software:
Mathematica
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