柱KDV方程的自相似解

Self-Similar Solutions of Cylindrical KDV Equation

对柱KDV方程进行相似变换、Miura变换等将其化为具有Painleve性质的非线性常微分方程,一是在此基础上,进一步将具有Painleve性质的非线性常微分方程弱化为Airy方程;二是引入Boutroux变换,使转化后的方程具有椭圆函数解,在这两种情况下分别得到了该方程的渐进自相似解.

By means of similar transformation and Miura transformation imposed on the cylindrical KDV equation,the equation is reduced to nonlinear ordinary differential equation with the property of Painleve. Based on this,the nonlinear ordinary differential equation with the property of Painleve is weakened to Airy equation and has elliptic function solutions under the Boutroux transformation. The asymptotic self-similar solutions of the equation are obtained under these two situations.