Acta Applicandae Mathematicae

, Volume 109, Issue 1, pp 151–196 | Cite as

Compatibility, Multi-brackets and Integrability of Systems of PDEs

  • Boris Kruglikov
  • Valentin Lychagin


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 δ-cohomology of generalized complete intersections and evaluate the formal functional dimension of the solutions space. The results are used to establish new integration methods.


Multi-brackets Jacobi-Mayer bracket Spencer cohomology Koszul homology Buchsbaum-Rim complex Integral Characteristics System of PDEs Symbols Compatibility 

Mathematics Subject Classification (2000)

35N10 58A20 58H10 35A30 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Mathematics and StatisticsUniversity of TromsøTromsøNorway

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