A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation
By Wenxiu Ma, Jyh-Hao Lee. 2009
639 citations recorded by the source corpus.
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 Backlund transformation.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/9dc3b09794bd118c1080f6a8796e691904925813
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In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Solving the (3 + 1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm (2012, background): “34), including traveling wave solutions and Grammian solutions, have been discussed in [47, 48].”
- A multiple exp-function method for nonlinear differential equations and its application (2010, background): “a unified approach to exact solutions to nonlinear equations has been proposed, revealing relations between solvable ordinary differential equations and nonlinear partial differential equations recently [17]. Solitary waves, periodic waves and kink waves modeling various nonlinear motions have been pre”