Two problems in the theory of differential equations
Mathematical Physics
2024-09-17 v1 math.MP
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?
Cite
@article{arxiv.1905.11754,
title = {Two problems in the theory of differential equations},
author = {Dimitry Leites},
journal= {arXiv preprint arXiv:1905.11754},
year = {2024}
}