On classification of discrete, scalar-valued Poisson brackets

@article{Parodi2012OnCO,
  title={On classification of discrete, scalar-valued Poisson brackets},
  author={E Emanuele Parodi},
  journal={Journal of Geometry and Physics},
  year={2012},
  volume={62},
  pages={2059-2076}
}
  • E. Parodi
  • Published 20 September 2011
  • Mathematics
  • Journal of Geometry and Physics

References

SHOWING 1-10 OF 24 REFERENCES

Differential-geometric Poisson brackets on a lattice

The concept of differential-geometric Poisson brackets (DGPB) was introduced in [i] in connection with an investigation of the properties of Poisson brackets of hydrodynamic type [2] and their

Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the

The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogoliubov-Whitham averaging method

Theorem 1. 1) Under local changes of the fields u = u(w) the coefficient g(u) in the bracket (2) transforms like a bilinear form (a tensor with upper indices); if det g 6= 0, then the expression b k

ON POISSON BRACKETS OF HYDRODYNAMIC TYPE

I. Riemannian geometry of multidimensional Poisson brackets of hydrodynamic type. In [1] we developed the Hamiltonian formalism of general onedimensional systems of hydrodynamic type. Now suppose

Lie bialgebras, Poisson Lie groups and dressing transformations

In this course, we present an elementary introduction, including the proofs of the main theorems, to the theory of Lie bialgebras and Poisson Lie groups and its applications to the theory of

Integrable Dynamical Systems Associated with the KdV Equation

An isospectral deformation representation is constructed for a countable set of dynamical systems with a quadratic nonlinearity, which become the Korteweg-de Vries equation in the continuum limit.

SOME CONSTRUCTIONS OF INTEGRABLE DYNAMICAL SYSTEMS

New constructions of integrable dynamical systems are found that admit representation as Lax matrix equations. A countable set of integrable systems is constructed which in the continuous limit turn

Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems

ContentsIntroduction Chapter I. Differential geometry of symplectic structures on loop spaces of smooth manifolds § 1.1. Symplectic and Poisson structures on loop spaces of smooth manifolds. Basic

Hamiltonian methods in the theory of solitons

The Nonlinear Schrodinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples

The Hamiltonian Structure of the Bogoyavlensky Lattice

We study the Hamiltonian structure of the Bogoyavlensky lattice, which is an integrable differential-difference equation and is a generalization of the Volterra model. We construct the lattice W