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arXiv · 1811.11830

Poisson pencils: reduction, exactness, and invariants

Paolo Lorenzoni·Marco Pedroni·Andrea Raimondo
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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.

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Paolo Lorenzoni, Marco Pedroni, Andrea Raimondo. 2019-02-07. Poisson pencils: reduction, exactness, and invariants. https://doi.org/10.1016/j.geomphys.2018.12.010

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