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math.DG2017
Higher order dispersive deformations of multidimensional Poisson brackets of hydrodynamic type
Matteo Casati
The theory of multidimensional Poisson vertex algebras (mPVAs) provides a completely algebraic formalism to study the Hamiltonian structure of PDEs, for any number of dependent and…
math.DG2017★ 4 cited
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…