非线性波方程求解的新方法

从Legendre椭圆积分和Jacobi椭圆函数的定义出发，得到了新的变换，并把它用于非线性演化方程的求解.用三个具体的例子，如非线性Klein-Gordon方程、Boussinesq方程和耦合的mKdV方程组，说明了具体的求解步骤.比较方便地得到非线性演化方程或方程组的新解析解，如周期解、孤子解等. 关键词： Jacobi椭圆函数 非线性方程 周期解 孤子解

A new method to construct solutions to nonlinear wave equations

From the definition of Legendre elliptic integration and Jacobi elliptic function, new transformations are obtained and applied to construct the exact solutions of nonlinear wave equations. The nonlinear Klein-Gordon equation, Boussinesq equation and the coupled mKdV equations are taken as three examples to illustrate the detailed steps in obtaining exact solutions. There new analytical solutions such as periodic solutions and soliton solutions are derived for these nonlinear evolution equation (or equations).