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Two Problems in the Theory Of Differential Equations

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Abstract

Differential equations considered in terms of exterior differential forms, as did É. Cartan, distinguish a differential ideal in the supercommutative superalgebra of differential forms, i.e., an affine supervariety. Therefore, each differential equation has a supersymmetry (perhaps trivial). Which superymmetries of systems of classical differential equations are not yet found? We also consider the question of why criteria of the formal integrability of differential equations are currently never used in practice.

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Authors and Affiliations

  1. Division of Science and Mathematics, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

    D. A. Leites

  2. Department of Mathematics, Stockholm University, Stockholm, Sweden

    D. A. Leites

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  1. D. A. Leites
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Correspondence to D. A. Leites.

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 198, No. 2, pp. 309–325, February, 2019.

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Leites, D.A. Two Problems in the Theory Of Differential Equations. Theor Math Phys 198, 271–283 (2019). https://doi.org/10.1134/S0040577919020089

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