KdV方程的Lie对称分析和精确*解

Lie symmetry analysis and exact explicit solutions for general KdV equation

运用李群方法对KdV方程作对称分析,求出方程的对称、对称约化和群不变解。进一步利用对称约化把方程化为常微分方程,同时结合首次积分和幂级数法,最终求出了方程的所有的显式精确解和解析解。

In this paper,symmetries,symmetry reductions and group invariant solutions to the general KdV equation are obtained by using the Lie group method.Furthermore,the general KdV equation is transformed into ordinary differential equation by using symmetry reductions and the first integral and power series method are employed simultaneously,the all exact explicit and analytic solutions are obtained finally.