We introduce a bracket on 1-forms defined on J ∞ (S 1,R n), i.e. the infinite jet extension of the space of loops, and prove that it satisfies the standard properties of a Poisson bracket. Using this bracket, we show that certain hierarchies appearing in the framework of F-manifolds with a compatible flat connection (M,∇, o) are Hamiltonian in a generalized sense. Moreover, we show that if a metric g compatible with ∇ is also invariant with respect to o, then this generalized Hamiltonian setup reduces to the standard one. © 2012 IOP Publishing Ltd.

Arsie, A., Lorenzoni, P. (2012). Poisson bracket on 1-forms and evolutionary partial differential equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 45(47) [10.1088/1751-8113/45/47/475208].

Poisson bracket on 1-forms and evolutionary partial differential equations

LORENZONI, PAOLO
2012

Abstract

We introduce a bracket on 1-forms defined on J ∞ (S 1,R n), i.e. the infinite jet extension of the space of loops, and prove that it satisfies the standard properties of a Poisson bracket. Using this bracket, we show that certain hierarchies appearing in the framework of F-manifolds with a compatible flat connection (M,∇, o) are Hamiltonian in a generalized sense. Moreover, we show that if a metric g compatible with ∇ is also invariant with respect to o, then this generalized Hamiltonian setup reduces to the standard one. © 2012 IOP Publishing Ltd.
Articolo in rivista - Articolo scientifico
Integrable PDEs; Hamiltonian formalism
English
2012
45
47
none
Arsie, A., Lorenzoni, P. (2012). Poisson bracket on 1-forms and evolutionary partial differential equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 45(47) [10.1088/1751-8113/45/47/475208].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/44712
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