On deformations of multidimensional Poisson brackets of hydrodynamic type

الأصل · EN

The theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consists of a pair (A,{·λ·}) of a differential algebra A and a bilinear operation called the λ-bracket. We extend the definition to the class of algebras A endowed with d≥1 commuting derivations. We call this structure a multidimensional PVA: it is a suitable setting to study Hamiltonian PDEs with d spatial dimensions. We apply this theory to the study of deformations of the Poisson brackets of hydrodynamic type for d=2.