2D viscoelastic equation from the perspective of Lie groups

TL;DR

This paper explores the symmetry properties of 2D viscoelastic equations using Lie group analysis, classifying their symmetries and reductions to facilitate understanding and solving these equations.

Contribution

It provides the first comprehensive symmetry classification and optimal Lie subalgebra system for 2D viscoelastic equations, advancing their analytical study.

Findings

Complete symmetry algebra for the equations

Classification of similarity reductions

Development of an optimal Lie subalgebra system

Abstract

We investigate 2-dimensional Viscoelastic equations with a view of Lie groups. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. Reductions of similarities related to subalgebras are classified.