Adam, Christoph; Sanchez-Guillen, Joaquin; Wereszczynski, Andrzej

Integrability and diffeomorphisms on target space

SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 123, 11 p., electronic only (2007)


Summary: We briefly review the concepts of generalized zero curvature conditions and integrability in higher dimensions, where integrability in this context is related to the existence of infinitely many conservation laws. Under certain assumptions, it turns out that these conservation laws are, in fact, generated by a class of geometric target space transformations, namely the volume-preserving diffeomorphisms. We classify the possible conservation laws of field theories for the case of a three-dimensional target space. Further, we discuss some explicit examples.

Mathematics Subject Classification

37K05, 37K30, 37K40, 58E50, 81R12, 81T10


integrability, zero curvature, conservation laws, nonlinear field theories