Integrability from an Abelian subgroup of the diffeomorphisms group

Journal Article · Wed Feb 15 04:00:00 EST 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2168400· OSTI ID:20768726

Adam, C; Sanchez-Guillen, J; Wereszczynski, A ^[1]

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1. Departamento de Fisica de Particulas, Facultad de Fisica, Universidad de Santiago, and Instituto Galego de Fisica de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela (Spain)

It has been known for some time that for a large class of nonlinear 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 fulfill, it should be useful in the study of those nonlinear field theories.

• OSTI ID: 20768726
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
EIKONAL APPROXIMATION
EQUATIONS
INTEGRAL CALCULUS
MINKOWSKI SPACE
NONLINEAR PROBLEMS
QUANTUM FIELD THEORY
SOLITONS
TWO-DIMENSIONAL CALCULATIONS