Frölicher structures, diffieties, and a formal KP hierarchy. (English) Zbl 1530.35012
Krasil’shchik, I. S. (ed.) et al., The diverse world of PDEs. Algebraic and cohomological aspects. Alexandre Vinogradov memorial conference. Diffieties, cohomological physics, and other animals, Independent University of Moscow and Moscow State University, Moscow, Russia, December 13–17, 2021. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 789, 183-196 (2023).
Summary: We propose a definition of a diffiety based on the theory of Frölicher structures. As a consequence, we obtain a natural Vinogradov sequence and, under the assumption of the existence of a suitable derivation on a given diffiety, we can form on it a Kadomtsev-Petviashvili hierarchy which is well-posed.
For the entire collection see [Zbl 1519.35008].
For the entire collection see [Zbl 1519.35008].
MSC:
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 54A10 | Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 58A20 | Jets in global analysis |
| 58A40 | Differential spaces |
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