标题： 一种变换有理函数方法和3+1维Jimbo-Miwa方程的精确解 显示英文标题

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

摘要： 提出了一种直接求解非线性偏微分方程精确解的方法，该方法利用有理函数变换。新方法在处理非线性方程的求解过程方面提供了更系统和方便的方式，统一了tanh函数类型方法、齐次平衡方法、exp函数方法、映射方法和F展开类型方法。其关键点是寻找从给定偏微分方程转换而来的变系数常微分方程的有理解。作为应用，处理了3+1维Jimbo-Miwa方程的精确解构造问题，以及一个Bäcklund变换。 显示英文摘要

摘要： 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 B\"acklund transformation.