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

TL;DR

This paper investigates reduction operators and constructs exact solutions for variable coefficient nonlinear wave equations with power nonlinearities, enhancing understanding of their symmetries and solution structures.

Contribution

It classifies regular reduction operators using generalized extended equivalence groups and constructs invariant exact solutions for specific models.

Findings

Classification of regular reduction operators

Construction of invariant exact solutions

Enhanced understanding of symmetries in variable coefficient wave equations

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.