Normal forms of dispersive scalar Poisson brackets with two independent variables |
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| Authors: | Guido Carlet Matteo Casati Sergey Shadrin |
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| Institution: | 1.IMB UMR 5584 CNRS Université Bourgogne Franche-Compté,Dijon,France;2.Istituto Nazionale d’Alta Matematica,Rome,Italy;3.Department of Mathematical Sciences,Loughborough University,Loughborough,UK;4.Korteweg-de Vries Instituut voor Wiskunde,Universiteit van Amsterdam,Amsterdam,The Netherlands |
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| 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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