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

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.

13 pages

References in corpus (2)

• On a family of solutions of the KP equation which also satisfy the Toda lattice hierarchy
• Explicit solutions to the Korteweg-de Vries equation on the half line

Cited by in corpus (8)

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• Comparison of a general series expansion method and the homotopy analysis method
• Efficient Numerical Scheme for Solving (1+1), (2+1)-dimensional and Coupled Burgers Equation
• Traveling Waves in Rational Expressions of Exponential Functions to the Conformable Time Fractional Jimbo-Miwa and Zakharov-Kuznetsov Equations
• Classical solution for the linear sigma model