二元Camassa-Holm方程的李对称分析和精确解

摘要

Using the Lie group analysis method,we study the two-component Camassa-Holm equation,which models shallow water waves moving over a linear shear flow.The similarity reductions and exact solutions for the equation are obtained.Then the power series solution are considered by using the power series method.Furthermore,the convergence of the power series solution to the equation is shown.The physical significance of the solutions is considered from the transformation group's point of view.%利用李群分析法研究二元Camassa-Holm方程,该方程以具有线性剪切流的浅水波为模型.通过对称分析得到方程的相似约化和精确解,再用幂级数法获得方程的解.证明了所得幂级数解的收敛性.从变换群的角度考虑了方程所得解的物理意义.