On natural invariants and equivalence of differential operators

TL;DR

This paper studies the rational differential invariants of nonlinear differential operators on smooth manifolds and applies these invariants to determine when such operators are equivalent.

Contribution

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

Findings

Characterization of the field of rational natural invariants.

Application to the equivalence problem of differential operators.

Framework for classifying nonlinear differential operators.

Abstract

We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of order $k\ge 2$ on a smooth manifold of dimension $n\ge 2$ and show their application to the equivalence problem of such operators.