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

摘要

A direct approach to exact solutions of nonlinear partial differentialequations is proposed, by using rational function transformations. The newmethod provides a more systematical and convenient handling of the solutionprocess of nonlinear equations, unifying the tanh-function type methods, thehomogeneous balance method, the exp-function method, the mapping method, andthe F-expansion type methods. Its key point is to search for rational solutionsto variable-coefficient ordinary differential equations transformed from givenpartial differential equations. As an application, the construction problem ofexact solutions to the 3+1 dimensional Jimbo-Miwa equation is treated, togetherwith a B\"acklund transformation.