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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Hamiltonian Operators of Dubrovin-Novikov Type in 2D

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