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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 198, Number 2, Pages 309–325
DOI: https://doi.org/10.4213/tmf9537 (Mi tmf9537) 		 
Two problems in the theory of differential equations

D. A. Leitesab

a Division of Science and Mathematics, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
b Department of Mathematics, Stockholm University, Stockholm, Sweden
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DOI: https://doi.org/10.4213/tmf9537
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.
Keywords: supersymmetry, nonholonomic mechanics.
Received: 29.01.2018
Revised: 26.07.2018
English version:
Theoretical and Mathematical Physics, 2019, Volume 198, Issue 2, Pages 271–283
DOI: https://doi.org/10.1134/S0040577919020089
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Document Type: Article
Language: Russian
Citation: D. A. Leites, “Two problems in the theory of differential equations”, TMF, 198:2 (2019), 309–325; Theoret. and Math. Phys., 198:2 (2019), 271–283
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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