On deformations of multidimensional Poisson brackets of hydrodynamic type

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dc.contributor.areaMathematicsen_US
dc.contributor.authorCasati, Matteo
dc.date.accessioned2013-12-10T09:44:02Z
dc.date.available2013-12-10T09:44:02Z
dc.date.issued2013-12-06
dc.description.abstractThe theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consist of a pair $(\mathcal{A},\{\cdot_{\lambda}\cdot\})$ of a differential algebra $\mathcal{A}$ and a bilinear operation called the $\lambda$-bracket. We extend the definition to the class of algebras $\mathcal{A}$ endowed with $d\geq 1$ commuting derivations. We call this structure a multidimensional PVA: it is a suitable setting to the study of deformations of the Poisson bracket of hydrodynamic type associated to the Euler's equation of motion of $d$-dimensional incompressible fluids. We prove that for $d=2$ all the first order deformations of such class of Poisson brackets are trivial.en_US
dc.description.tableofcontents1. Introduction 1.1 Poisson Vertex Algebras 1.2 Poisson brackets of hydrodynamic type and their deformations 2. Multidimensional Poisson Vertex Algebras 2.1 Formal map space 2.2 Poisson bivector and Poisson brackets 2.3 Poisson Vertex Algebras 2.4 Proof of Master formula 2.5 Cohomology of Poisson Vertex Algebras 3. Multidimensional Poisson brackets of hydrodynamic type 3.1 Deformation of Lie-Poisson bracket of hydrodynamic type 3.2 Proof of Theorem 5 4. Concluding remarksen_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/7235
dc.language.isoenen_US
dc.miur.area1en_US
dc.publisherSISSAen_US
dc.relation.ispartofseriesarXiv:1312.1878;
dc.subject.keywordHamiltonian operatoren_US
dc.subject.keywordHydrodynamic Poisson bracketen_US
dc.subject.keywordPoisson Vertex Algebraen_US
dc.subject.miurMAT/07 FISICA MATEMATICA
dc.titleOn deformations of multidimensional Poisson brackets of hydrodynamic typeen_US
dc.typePreprinten_US
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