Natural differential invariants and equivalence of third order nonlinear differential operators

TL;DR

This paper studies the rational natural differential invariants of third order nonlinear differential operators on two-dimensional manifolds and applies these invariants to determine when such operators are equivalent.

Contribution

It provides a description of the field of invariants for these operators and demonstrates their use in solving the equivalence problem.

Findings

Characterization of the field of rational natural differential invariants.

Application of invariants to the equivalence problem.

Framework for classifying third order nonlinear differential operators.

Abstract

We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third order on a two dimensional manifold and show their application to the equivalence problem of such operators.