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Normal forms of dispersive scalar Poisson brackets with two independent variables
Guido Carlet, Matteo Casati, Sergey Shadrin
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…
Central invariants revisited
Guido Carlet, Reinier Kramer, Sergey Shadrin
We use refined spectral sequence arguments to calculate known and previously unknown bi-Hamiltonian cohomology groups, which govern the deformation theory of semi-simple bi-Hamilto…
Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets
Guido Carlet, Matteo Casati, Sergey Shadrin
We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with independent variables. We find that the second and third cohomology groups are gener…
The bi-Hamiltonian cohomology of a scalar Poisson pencil
Guido Carlet, Hessel Posthuma, Sergey Shadrin
We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the KdV case, we obtai…
Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed
Guido Carlet, Hessel Posthuma, Sergey Shadrin
We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dis…
Bihamiltonian cohomology of KdV brackets
Guido Carlet, Hessel Posthuma, Sergey Shadrin
Using spectral sequences techniques we compute the bihamiltonian cohomology groups of the pencil of Poisson brackets of dispersionless KdV hierarchy. In particular this proves a co…