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A transformed rational function method and exact solutions to the $3+1$ dimensional Jimbo-Miwa equation. (English) Zbl 1198.35231
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. 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:
35Q53KdV-like (Korteweg-de Vries) equations
35A30Geometric theory for PDE, characteristics, transformations
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RATH
WorldCat.org
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References:
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