用近似同伦对称法求解阻尼KdV方程

摘要

应用近似同伦对称方法对阻尼KdV方程进行约化并求得近似解.为阻尼KdV方程选取一个同伦模型,其近似解可以用级数形式表示;再应用近似对称法,可以将其方程约化为若干个3阶ODE方程.近似同伦对称方法适用于一类强扰动非线性微分方程.%The damping DdV equation is investigated via the approximate homotopy symmdtry method and the approximation is obtained. A Homotopy model is selected, then the approximate symmetry and similarity reduction equations of different orders are derived and the corresponding series reduction solutions are obtained. Approximate homotopy symmetry method can be applied to some other strong perturbed nonlinear differential equations.