Integrability from an abelian subgroup of the diffeomorphism group

TL;DR

The paper introduces a weaker integrability condition for certain non-linear field theories, leading to infinitely many conservation laws linked to an abelian subgroup of area-preserving diffeomorphisms, simplifying their analysis.

Contribution

It identifies a new, weaker integrability condition that still yields infinite conservation laws, expanding the understanding of integrable submodels in non-linear field theories.

Findings

Existence of a weaker integrability condition for these theories.

Conservation laws related to an abelian subgroup of diffeomorphisms.

Simplification in studying non-linear field theories.

Abstract

It has been known for some time that for a large class of non-linear field theories in Minkowski space with two-dimensional target space the complex eikonal equation defines integrable submodels with infinitely many conservation laws. These conservation laws are related to the area-preserving diffeomorphisms on target space. Here we demonstrate that for all these theories there exists, in fact, a weaker integrability condition which again defines submodels with infinitely many conservation laws. These conservation laws will be related to an abelian subgroup of the group of area-preserving diffeomorphisms. As this weaker integrability condition is much easier to fulfil, it should be useful in the study of those non-linear field theories.