Normal forms of dispersive scalar Poisson brackets with two independent variables

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 Miu...

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Detalles Bibliográficos
Autores principales: Carlet, Guido, Casati, Matteo, Shadrin, Sergey
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6133259/
https://www.ncbi.nlm.nih.gov/pubmed/30220777
http://dx.doi.org/10.1007/s11005-018-1076-x
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author Carlet, Guido
Casati, Matteo
Shadrin, Sergey
author_facet Carlet, Guido
Casati, Matteo
Shadrin, Sergey
author_sort Carlet, Guido
collection PubMed
description 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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spelling pubmed-61332592018-09-14 Normal forms of dispersive scalar Poisson brackets with two independent variables Carlet, Guido Casati, Matteo Shadrin, Sergey Lett Math Phys Article 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. Springer Netherlands 2018-03-26 2018 /pmc/articles/PMC6133259/ /pubmed/30220777 http://dx.doi.org/10.1007/s11005-018-1076-x Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Carlet, Guido
Casati, Matteo
Shadrin, Sergey
Normal forms of dispersive scalar Poisson brackets with two independent variables
title Normal forms of dispersive scalar Poisson brackets with two independent variables
title_full Normal forms of dispersive scalar Poisson brackets with two independent variables
title_fullStr Normal forms of dispersive scalar Poisson brackets with two independent variables
title_full_unstemmed Normal forms of dispersive scalar Poisson brackets with two independent variables
title_short Normal forms of dispersive scalar Poisson brackets with two independent variables
title_sort normal forms of dispersive scalar poisson brackets with two independent variables
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6133259/
https://www.ncbi.nlm.nih.gov/pubmed/30220777
http://dx.doi.org/10.1007/s11005-018-1076-x
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AT casatimatteo normalformsofdispersivescalarpoissonbracketswithtwoindependentvariables
AT shadrinsergey normalformsofdispersivescalarpoissonbracketswithtwoindependentvariables

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