The natural extension to PDEs of Lie's reduction of order algorithm for ODEs

TL;DR

This paper extends Lie's reduction of order algorithm from ordinary differential equations to partial differential equations using symmetry-based methods, providing new insights and examples.

Contribution

It introduces a symmetry-based approach that generalizes Lie's reduction algorithm from ODEs to PDEs, offering a new perspective and practical examples.

Findings

The symmetry-based method effectively finds nonlocally related systems for PDEs.

The approach generalizes Lie's reduction algorithm to PDEs.

Multiple examples demonstrate the method's applicability.

Abstract

In this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-based method for partial differential equations is the natural extension of Lie's reduction of order algorithm for ordinary differential equations by looking at this algorithm from a different point of view. Many examples exhibit various situations that can arise.