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A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation

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  • Ma, Wen-Xiu
  • Lee, Jyh-Hao

Abstract

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.

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  • Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1356-1363
    DOI: 10.1016/j.chaos.2009.03.043
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