2+1维破裂孤子方程的新孤子解

New soliton solutions to 2+1 dimensional breaking soliton equation

李群方法是研究非线性微分方程的有力工具,应用经典或非经典李对称方法可得到大量非线性微分方程(组)的显式解．对于2+1维的破裂孤子方程,利用CK方法得到了方程求解的Bachlund变换公式,从而获得方程的一些新精确解,推广了文献[4—8]中的结果。

The Lie group method is a powerful tool to study the nonlinear differentical equa- tions. By using the classical or nonclassical Lie symmetry method we can get amount of exact solutions of the nonlinear differential equations. For the breaking soliton equation, by applying the CK method, we obtain the Backlund transformation of finding solution, so some new solutions are found. We generalize the results in the paper [4-8].