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Zbl 1198.35231
Ma, Wen-Xiu; Lee, Jyh-Hao
A transformed rational function method and exact solutions to the $3+1$ dimensional Jimbo-Miwa equation. (English)
[J] Chaos Solitons Fractals 42, No. 3, 1356-1363 (2009). ISSN 0960-0779

Summary: A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanh-function type methods, the homogeneous balance method, the exp-function method, the mapping method, and the $F$-expansion type methods. Its key point is to search for rational solutions to variable-coefficient ordinary differential equations transformed from given partial differential equations. As an application, the construction problem of exact solutions to the 3+1 dimensional Jimbo-Miwa equation is treated, together with a Bäcklund transformation. \par Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC 2000:: *35Q53 KdV-like equations
35A30 Geometric theory for PDE, transformations

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Zentralblatt MATH Berlin [Germany]