Compatibility, multi-brackets and integrability of systems of PDEs

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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.
Some modifications in sections 6.1-2; new references're added

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Differential Geometry, Analysis of PDEs, 35N10, 58A20, 58H10 (Primary); 35A30 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/155157

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610930
 http://arxiv.org/abs/math/0610930

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arXiv