（2＋1）维 Calogero-Bogoyavlenskii-Schiff方程新的精确解

摘要

基于李群理论，利用改进的CK 直接法求解（2＋1）维 Calogero‐Bogoyavlenskii‐Schiff 方程，得到该方程的一般对称群，并以此为基础约化该方程得到低维微分方程。借助辅助函数法求解所得约化方程，得到该方程的一些新的精确解。该方法给出了方程的新解与旧解之间的联系，也适用于其他的非线性演化方程。%The modified CK direct method ,based on the lie group theory ,was applied to solve the equation of (2 + 1 )‐dimensional Calogero‐Bogoyavlenskii‐Schiff and a general symmetry group was obtained .The equation was further reduced until it became a low‐dimensional equa‐tion .Some new exact solutions were achieved from the obtained reducted equation with the aux‐iliary function .This method identifies the link between the new and the old solutions ,and can be applied to the non‐linear evolution equation .