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math.DG2006★ 9 cited
Dimension of the solutions space of PDEs
Boris Kruglikov, Valentin Lychagin
We discuss the dimensional characterization of the solutions space of a formally integrable system of partial differential equations and provide certain formulas for calculations o…
math.DG2006★ 2 cited
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-b…
math.DG2006
Abelian Equations and Rank Problems for Planar Webs
Vladislav V. Goldberg, Valentin V. Lychagin
We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its cu…