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

Wen-Xiu Ma and Jyh-Hao Lee

Chaos, Solitons & Fractals, 2009, vol. 42, issue 3, 1356-1363

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.

Date: 2009
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Citations: View citations in EconPapers (17)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:42:y:2009:i:3:p:1356-1363

DOI: 10.1016/j.chaos.2009.03.043

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