# 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}
}
• M. Casati
• Published 6 December 2013
• Mathematics
• Communications in Mathematical Physics
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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