Compatibility, multi-brackets and integrability of systems of PDEs
Differential Geometry
2008-02-20 v2 Analysis of PDEs
Abstract
We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators. These multi-brackets generalize the higher Jacobi-Mayer brackets, important in the study of evolutionary equations and the integrability problem. We also calculate Spencer delta-cohomology of generalized complete intersections and evaluate the formal functional dimension of the solutions space. The results are applied to establish new integration methods and solve several differential-geometric problems.
Keywords
Cite
@article{arxiv.math/0610930,
title = {Compatibility, multi-brackets and integrability of systems of PDEs},
author = {Boris Kruglikov and Valentin Lychagin},
journal= {arXiv preprint arXiv:math/0610930},
year = {2008}
}
Comments
Some modifications in sections 6.1-2; new references're added