Nonclassical symmetries of a class of nonlinear partial differential equations and compatibility

Abstract. Symmetries play an important role in solving partial differential equations. In this paper, the de-termining equations for a class of nonlinear partial differential equations with arbitrary order are considered. It is shown that the determining equations for the nonclassical reduction can be obtained by requiring the compatibility between the original equation and the invariant surface condition. A simple partial differential equation and BBM equation serve as examples to illustrating the feasibility of this method