Integrability from an abelian subgroup of the diffeomorphism group

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.

13 pages, Latex file

References in corpus (4)

• Toroidal Solitons in Nicole-type Models
• Generalized Eikonal Knots and New Integrable Dynamical Systems
• Generalized integrability conditions and target space geometry
• Knots, Braids and Hedgehogs from the Eikonal Equation

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