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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.

参考文献

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[11] Lou S Y,Ma H C.Non-Lie symmetry groups of 2+1 dimensional nonlinear systems obtained from a simple direct method[J].J.Phys.A:Math.Gen.,2005,38:L129-L137.
[12] Ma H C.A simple method to general Lie point symmetry groups of the 3+1 dimensional Jimbo-Miwa equation[J].Chin.Phys.Lett.,2005,22:554-557.
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[14] Tian Guichen,Liu Xiqiang.Exact solutions of the general variable coefficient KdV equation with external force term[J].Chinese Journal of Quantum Electronics(量子电子学报),2005,22(3):339-343(in Chinese).
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