Contact Equivalence Problem for Linear Parabolic Equations

TL;DR

This paper uses the moving coframe method to analyze the contact equivalence problem for linear parabolic equations, deriving structure equations and invariants to classify these equations under contact transformations.

Contribution

It provides a complete solution to the local equivalence problem for linear parabolic equations using differential invariants and structure equations.

Findings

Derived structure equations for the symmetry groups.

Identified complete sets of differential invariants.

Solved the equivalence problem in terms of these invariants.

Abstract

The moving coframe method is applied to solve the local equivalence problem for the class of linear parabolic equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and the complete sets of differential invariants for symmetry groups are found. The solution of the equivalence problem is given in terms of these invariants.