Poisson pencils: Reduction, exactness, and invariants

JOURNAL OF GEOMETRY AND PHYSICS

卷:138

Article

Lorenzoni, Paolo¹  Pedroni, Marco²  Raimondo, Andrea² 

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Roberto Cozzi 55, I-20125 Milan, Italy

[2] Univ Bergamo, Dipartimento Ingn Gest Informaz & Prod, Viale Marconi 5, I-24044 Dalmine, BG, Italy

关键词: Drinfeld-Sokolov reduction;    Poisson pencils of hydrodynamic type;    Central invariants;    Integrable PDEs;    Exact bi-Hamiltonian manifolds;   

DOI  :  10.1016/j.geomphys.2018.12.010

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free