一类非线性偏微分方程的非古典对称和相容性

Nonclassical Symmetries and Compatibility of a Class of Partial Differential Equations

研究了一类任意阶的非线性偏微分方程的非古典对称的决定方程,并以一偏微分方程为例,运用向量场和其延拓以及不变表面条件和初始方程的相容性两种方法得出了相同的非古典对称的决定方程,由此得到了利用不变条件和初始方程的相容性也可求得非线性偏微分方程的非古典对称的重要结论。最后以Collapse方程为例,证明了该结论的可靠性。

The determining equations for the nonclassical symmetries of a class of nonlinear classical parnal differential equations with arbitrary orders are studied. A partial differential equation is quoted to get the conclusion that the nonclassocal symmetries of the nonlinear partial differential equations can be derived by using the compatibility between the original equation and the invariant surface condition. Finally, the collapse equation is discussed to proved the conclusion.