Boussinesq方程的Jacobi椭圆函数精确解

Exact solutions of jacobi elliptic function for boussinesq equation

对Jacobi椭圆函数展开法进行了深入研究,提出一种扩展的Jacobi椭圆函数展开法,在符号计算软件Maple下,对Boussinesq方程求解,得到该方程形式更为丰富的Jacobi椭圆函数周期解,其中包括一些新解.在极限情况下,一部分解退化为三角函数解和孤立波解。另外,该方法能应用到其他的非线性发展方程。

By investigating the Jacobi elliptic function expansion method carefully, an extended Jacobi elliptic function expansion method is proposed and successfully applied to Boussinesq equation with the aid of symbolic computation system Maple. Abundant exact periodic solutions including some new solution is obtained. A few corresponding trigonometric function solutions and solitary wave solutions are also obtained at the modulus m→0 and m→1. In addition, the new method can also be applied to other nonlinear evolution equations.