一类组合方程的势对称分类

SYMMETRY CLASSIFICATION FOR A CLASS OF COMBINED EQUATIONS

首先给出一类含有任意函数的变系数波动方程u_(xx)=H(x)u_(tt)的古典对称及其势对称的完全分类,然后借助于这个波动方程的对称分类,系统讨论了含有两个任意函数的一类组合方程的势对称分类,所得结果确实扩充了原方程的对称.在计算过程中,采用微分形式的吴方法,微分特征列的程序包起到了重要作用.

By means of differential Wu-method, the classical symmetry and potential symmetry classification of a variable-coefficient wave equations uxx = H（x）utt with a arbitrary function is investigated. Then the potential symmetry classification of a class of partial differential equations which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations is obtained based on the above classification. Moreover, some new symmetries of the combined equations are derived. These symmeties extend the symmetries of original equations safely. Here, differential characteristic set package plays an important role in the calculation.