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

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.

Proc. 7th International Workshop "Quantum Theory and Symmetries-7" (August 7-13, 2011; CVUT Prague, Czech Republic), 20 pages

References in corpus (3)

• Algebraic properties of Gardner's deformations for integrable systems
• Variational Poisson-Nijenhuis structures for partial differential equations
• Variational Lie algebroids and homological evolutionary vector fields

Cited by in corpus (2)

• The geometry of variations in Batalin-Vilkovisky formalism
• The calculus of multivectors on noncommutative jet spaces