# 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)

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https://doi.org/10.1007/s11005-018-1076-x

## Abstract

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 10.1007/s11005-018-1076-x Poisson brackets, Poisson cohomology, Hamiltonian operator, Miura transformation Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Matteo Casati 17 Aug 2018 14:23 UTC 11 Jul 2019 13:20 UTC https://kar.kent.ac.uk/id/eprint/67926 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-2207-4807