Reduction operators and exact solutions of variable coefficient nonlinear wave equations with power nonlinearities

Abstract

Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A classification of regular reduction operators is performedwith respect to generalized extended equivalence groups. Exact solutions of some nonlinear wave model which are invariant under certain reduction operators are also constructed.