# On Deformations of Multidimensional Poisson Brackets of Hydrodynamic Type

@article{Casati2013OnDO, title={On Deformations of Multidimensional Poisson Brackets of Hydrodynamic Type}, author={Matteo Casati}, journal={Communications in Mathematical Physics}, year={2013}, volume={335}, pages={851-894} }

The theory of Poisson vertex algebras (PVAs) (Barakat et al. in Jpn J Math 4(2):141–252, 2009) is a good framework to treat Hamiltonian partial differential equations. A PVA consists of a pair $${(\mathcal{A},\{\cdot_\lambda\cdot\})}$$(A,{·λ·}) of a differential algebra $${\mathcal{A}}$$A and a bilinear operation called the $${\lambda}$$λ -bracket. We extend the definition to the class of algebras $${\mathcal{A}}$$A endowed with $${d \geq 1}$$d≥1 commuting derivations. We call this structure a…

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### Higher-Order Dispersive Deformations of Multidimensional Poisson Brackets of Hydrodynamic Type

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