On a new procedure for finding nonclassical symmetries

Abstract

A new technique for deriving the determining equations of nonclassical symmetries associated with a partial differential equation system is introduced. The problem is reduced to computing the determining equations of the classical symmetries associated with a related equation with coefficients which depend on the nonclassical symmetry operator. As a consequence, all the symbolic manipulation programs designed for the latter task can also be used to find the determining equations of the nonclassical symmetries, without any adaptation of the program. The algorithm was implemented as the maple routine gendefnc and uses the maple package desolv (authors Carminati and Vu). As an example, we consider the Huxley partial differential equation.