求非线性系统对称群的新方法

New methods for finding symmetry groups of nonlinear systems

(1)从Lax可积系统的Lax对出发,寻找非线性系统的对称及精确解,利用这种方法可以解决不少(2+1)维的可积系统,它的优点在于比较简洁方便,这从KP方程的求解对比就可以看出.(2)从CK直接法入手,将这种方法进行修正,利用这种修正的CK直接法求非线性系统的对称和精确解;这种方法的最大优点在于不但可以用于可积系统,而且也适用于不可积系统,还可以求出离散群.另外,这种方法也适用于高维的不可积模型.

At first,we obtain the symmetry and exact solution of nonlinear integral system using Lax pair which can be used to solve many(2+1)-dimensional integral systems in a simple and convenient way as observed from the KP equation.In addition,we use the modified CK direct method to acquire the symmetry and exact solution which can be applied in both integral and non-integral systems.Along with this process,the discrete group can be obtained for dealing with the high dimensional system.