Differential invariants for a class of diffusion equations

TL;DR

This paper determines the full symmetry group of a class of (1+1)-dimensional diffusion equations and constructs differential invariants using the moving frame method, advancing the understanding of their symmetry properties.

Contribution

It introduces a complete equivalence group for a class of second-order evolution equations and applies the moving frame method to find differential invariants.

Findings

Identified the infinite-dimensional equivalence group.

Constructed a moving frame for the group.

Derived a minimal generating set of differential invariants.

Abstract

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the normalization procedure, a moving frame for a group related to the equivalence group in the context of equivalence transformations among equations of the class under consideration. Using the moving frame constructed, we describe the algebra of differential invariants of the former group by obtaining a minimum generating set of differential invariants and a complete set of independent operators of invariant differentiation.