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Normal forms of dispersive scalar Poisson brackets with two independent variables

Carlet, Guido, Casati, Matteo, Shadrin, Sergey (2018) Normal forms of dispersive scalar Poisson brackets with two independent variables. Letters in Mathematical Physics, . ISSN 0377-9017. (doi:10.1007/s11005-018-1076-x) (KAR id:67926)


We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well-known triviality result exists, the Miura equivalence classes are parametrised by an infinite number of constants, which we call numerical invariants of the brackets. We obtain explicit formulas for the first few numerical invariants.

Item Type: Article
DOI/Identification number: 10.1007/s11005-018-1076-x
Uncontrolled keywords: Poisson brackets, Poisson cohomology, Hamiltonian operator, Miura transformation
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Matteo Casati
Date Deposited: 17 Aug 2018 14:23 UTC
Last Modified: 10 Dec 2022 03:02 UTC
Resource URI: (The current URI for this page, for reference purposes)

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