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On Deformation of Poisson Manifolds of Hydrodynamic Type

✍ Scribed by Luca Degiovanni; Franco Magri; Vincenzo Sciacca


Publisher
Springer
Year
2004
Tongue
English
Weight
205 KB
Volume
253
Category
Article
ISSN
0010-3616

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Reduction in the category of Poisson manifolds is defined and some basic properties are derived. The context is chosen to include the usual theorems on reduction of symplectic manifolds, as well as results such as the Dirac bracket and the reduction to the Lie-Poisson bracket.

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In this paper we study the deformations of bi-Hamiltonian PDEs of hydrodynamic type with one dependent variable. The reason we study such deformations is that the deformed systems maintain an infinite number of commuting integrals of motion up to a certain order in the deformation parameter. This fa