On a reduction of nonlinear evolution and wave type equations via non-point symmetry method

TL;DR

This paper introduces a method combining non-point and conditional symmetries to reduce nonlinear evolution and wave equations, enabling the construction of solutions and Bäcklund transformations, applicable to various PDEs.

Contribution

It presents a novel approach that integrates non-point and conditional symmetries for solving and transforming nonlinear PDEs.

Findings

Method constructs solutions for nonlinear PDEs.

Enables derivation of Bäcklund transformations.

Applicable to non-evolutionary PDEs.

Abstract

We study the symmetry reduction of nonlinear evolution and wave type differential equations by using operators of non-point symmetry. In our approach we use both operators of classical and conditional symmetry. It appears that the combination of non-point and conditional symmetry enables us to construct not only solutions but B\"acklund transformations too for the equation under study. We show that the method can be applied to nonevolutionary partial differential equations.