Non-local Poisson structures and applications to the theory of integrable systems

@article{Sole2013NonlocalPS,
  title={Non-local Poisson structures and applications to the theory of integrable systems},
  author={A. Sole and V. Kac},
  journal={Japanese Journal of Mathematics},
  year={2013},
  volume={8},
  pages={233-347}
}
  • A. Sole, V. Kac
  • Published 2013
  • Physics, Mathematics
  • Japanese Journal of Mathematics
  • We develop a rigorous theory of non-local Poisson structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee applicability of the Lenard–Magri scheme of integrability to a pair of compatible non-local Poisson structures. We apply this scheme to several such pairs, proving thereby integrability of various evolution equations, as well as hyperbolic equations. 

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