Normal forms of dispersive scalar Poisson brackets with two independent variables

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.
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https://hal.archives-ouvertes.fr/hal-01899984
Contributor : Sébastien Mazzarese <>
Submitted on : Saturday, October 20, 2018 - 4:25:45 PM
Last modification on : Thursday, December 20, 2018 - 8:49:34 AM

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Guido Carlet, Matteo Casati, Sergey Shadrin. Normal forms of dispersive scalar Poisson brackets with two independent variables. Letters in Mathematical Physics, Springer Verlag, 2018, 108 (10), pp.2229-2253. ⟨10.1007/s11005-018-1076-x⟩. ⟨hal-01899984⟩

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