离散修正KdV方程的解析近似解

Analytic approximation for the soliton solution of the discrete modified KdV equation

将同伦分析法进行了推广,使之适用于求解离散修正KdV方程.获得了由指数函数表达的亮孤子解,该解析近似解与精确解符合很好.数值模拟结果说明了同伦分析法对求解复杂非线性问题的有效性和潜力.

We extend the homotopy analysis method to solving the discrete modified KdV equation. The bright soliton solution expressed by a series of exponential functions is obtained,which agrees well with the exact solution. It indicates the validity and great potential of the homotopy analysis method in solving complicated nonlinear problems.