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arXiv · 1905.11754

Two problems in the theory of differential equations

Dimitry Leites
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Abstract

1) The differential equation considered in terms of exterior differential forms, as \'E.Cartan did, singles out a differential ideal in the supercommutative superalgebra of differential forms, hence an affine supervariety. In view of this observation, it is evident that every differential equation has a supersymmetry (perhaps trivial). Superymmetries of which (systems of) classical differential equations are missed yet? 2) Why criteria of formal integrability of differential equations are never used in practice?

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Dimitry Leites. 2019-05-28. Two problems in the theory of differential equations. https://doi.org/10.1134/s0040577919020089

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