利用Jacobi椭圆函数展开法求解特殊类型的方程

Applications of Jacobi Elliptic Function Expansion Method to Several Special Nonlinear Equations

利用未知函数的变换,将非线性演化方程转换为以新未知函数及其偏导数为变元的多项式型的非线性偏微分方程,再应用Jacobi椭圆函数展开法,求解sine-Gordon方程和Dodd-Bullough-Mikhailov方程的精确周期解,所得的周期解包含孤波解.该方法同样适用于求解其他非线性演化方程.

By transformation of a dependent variable, a nonlinear evolution equation （NLEE） is converted into a nonlinear partial differential equation （NPDE） with a polynomial type of a new dependent variable and its partial derivatives. A Jacobi elliptic function expansion method is proposed to construct the exact periodic solutions of several nonlinear equations--sine-Gordon equation and Dodd-Bullough- Mikhailov equation. Periodic solutions obtained with this method include the solitary solutions and the shock wave solutions. The method can also be applied to other nonlinear evolution equations.