On the symmetry approach to reduction of partial differential equations

TL;DR

This paper introduces a symmetry reduction method for partial differential equations, reducing their variables, and provides generalized conditions ensuring solutions are invariant in the classical sense.

Contribution

It presents a new symmetry reduction approach and generalized conditions for invariant solutions in the context of PDEs.

Findings

Developed a symmetry reduction method for PDEs.

Derived generalized conditions for invariant solutions.

Enhanced understanding of solution invariance in PDEs.

Abstract

We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by conditional symmetry method to be an invariant one in classical sense.