Geometry of jet spaces and integrable systems
Differential Geometry
2012-12-19 v6 Mathematical Physics
Analysis of PDEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space of infinite jets) and with constraints (on a PDE) are discussed. Analogs of tangent and cotangent bundles to a differential equation are introduced and the variational Schouten bracket is defined. General theoretical constructions are illustrated by a series of examples.
Cite
@article{arxiv.1002.0077,
title = {Geometry of jet spaces and integrable systems},
author = {Joseph Krasil'shchik and Alexander Verbovetsky},
journal= {arXiv preprint arXiv:1002.0077},
year = {2012}
}
Comments
54 pages; v2-v6 : minor corrections