Lie symmetries for systems of evolution equations

TL;DR

This paper investigates Lie symmetries of systems of evolution equations within a bimetric space framework, linking symmetries to geometric collineations, thus advancing the understanding of symmetry structures in differential equations.

Contribution

It establishes a novel connection between Lie symmetries of evolution equations and collineations in bimetric spaces, providing a geometric perspective.

Findings

Identifies the relation between Lie symmetries and collineations in bimetric spaces

Provides a geometric characterization of symmetries for evolution equations

Enhances the theoretical framework for symmetry analysis in differential equations

Abstract

The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined