改进的截断展开法和变系数mKdV方程新的精确类孤子解

Improved Truncated Expansion Method and Exact Solutions the General Variable Coefficent mKdV Equation

本文利用改进的截断展开法,求出了广义变系数mKdV方程的精确解。首先,通过行波变换,将偏微分方程转化为常微分方程。然后在截断展开中采用了非线性Riccati方程F=pF+qF+rF2将复杂的变系数非线性转化为一组超定代数方程组。由此求出给定方程的精确孤子解。

Exact solitary solutions for the generalized mKdV equation with variable coefficients are obtained by the use of improved truncated expansion method.First,with the aid of traveling wave transformation,partial differential equation is reduced to an ordinary differential equation.Then,in the truncated expansion method,using non-linear Riccatic equation F =pF＋qF＋rF 2 changes the problem solving an ordinary differential equation into another one solving the corresponding set of nonlinear algebraic equations.Thus,the exact solitude-like solutions to the given equations are obtained.