Abelian Lie symmetry algebras of two-dimensional quasilinear evolution equations

TL;DR

This paper classifies abelian Lie symmetry algebras of two-dimensional second-order quasilinear evolution equations, identifying conditions under which these equations are linearizable based on the dimension and rank of their symmetry algebras.

Contribution

It provides a complete classification of abelian Lie symmetry algebras for these equations and establishes criteria for their linearizability.

Findings

Equations with abelian Lie symmetry algebra of dimension ≥5 are linearizable.

Equations with abelian Lie symmetry algebra of dimension ≥3 and rank 1 are linearizable.

Classification aids in understanding symmetry properties of two-dimensional quasilinear evolution equations.

Abstract

We carry out the classification of abelian Lie symmetry algebras of two-dimensional second-order nondegenerate quasilinear evolution equations. It is shown that such an equation is linearizable if it admits an abelian Lie symmetry algebra that is of dimension greater than or equal to five or of dimension greater than or equal to three with rank one.