We study the invariants (in particular, the central invariants) of suitable Poisson pencils from the point of view of the theory of bi-Hamiltonian reduction, paying a particular attention to the case where the Poisson pencil is exact. We show that the exactness is preserved by the reduction. In the Drinfeld–Sokolov case, the same is true for the characteristic polynomial of the pencil, which plays a crucial role in the definition of the central invariants. We also discuss the bi-Hamiltonian structures of a generalized Drinfeld–Sokolov hierarchy and of the Camassa–Holm equation.

Lorenzoni, P., Pedroni, M., Raimondo, A. (2019). Poisson pencils: Reduction, exactness, and invariants. JOURNAL OF GEOMETRY AND PHYSICS, 138, 154-167 [10.1016/j.geomphys.2018.12.010].

Poisson pencils: Reduction, exactness, and invariants

Lorenzoni, P;Pedroni, M;Raimondo, A
2019

Abstract

We study the invariants (in particular, the central invariants) of suitable Poisson pencils from the point of view of the theory of bi-Hamiltonian reduction, paying a particular attention to the case where the Poisson pencil is exact. We show that the exactness is preserved by the reduction. In the Drinfeld–Sokolov case, the same is true for the characteristic polynomial of the pencil, which plays a crucial role in the definition of the central invariants. We also discuss the bi-Hamiltonian structures of a generalized Drinfeld–Sokolov hierarchy and of the Camassa–Holm equation.
Articolo in rivista - Articolo scientifico
Central invariants; Drinfeld–Sokolov reduction; Exact bi-Hamiltonian manifolds; Integrable PDEs; Poisson pencils of hydrodynamic type; Mathematical Physics; Physics and Astronomy (all); Geometry and Topology
English
154
167
14
Lorenzoni, P., Pedroni, M., Raimondo, A. (2019). Poisson pencils: Reduction, exactness, and invariants. JOURNAL OF GEOMETRY AND PHYSICS, 138, 154-167 [10.1016/j.geomphys.2018.12.010].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/251796
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