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Geometry of jet spaces and integrable systems. (English) Zbl 1230.58005

From the authors’ 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.

MSC:

58A20 Jets in global analysis
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
35Q70 PDEs in connection with mechanics of particles and systems of particles
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References:

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