Compatibility, multi-brackets and integrability of systems of PDEs
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 applied to establish new integration methods and solve several differential-geometric problems.
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CitationActa Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications DOI 10.1007/s10440-009-9446-0
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