Integrability from an abelian subgroup of the diffeomorphism group

Details Integrability from an abelian subgroup of the diffeomorphism group Integrability from an abelian subgroup of the diffeomorphism group

2005-11-28

arxiv.org/abs/hep-th/0511277v1

J.Math.Phys.47:022303,2006

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, Latex file

Scientific paper

10.1063/1.2168400

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.

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