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arXiv · 1111.3272

Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models

Arthemy V. Kiselev
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Abstract

We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson formalism (e.g., for equations of Korteweg-de Vries type), geometry of Liouville-type hyperbolic systems (including the 2D Toda chains), and Euler-Lagrange gauge theories (such as the Yang-Mills theories, gravity, or the Poisson sigma-models). Also, we formulate several open problems.

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Arthemy V. Kiselev. 2011-11-14. Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models. https://doi.org/10.1088/1742-6596/343/1/012058

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