Poisson brackets of mappings obtained as ( q, p) reductions of lattice equations
Abstract
In this paper, we present Poisson brackets of certain classes of mappings obtained as general periodic reductions of integrable lattice equations. The Poisson brackets are derived from a Lagrangian, using the socalled Ostrogradsky transformation. The ( q, p) reductions are ( p + q)dimensional maps and explicit Poisson brackets for such reductions of the discrete KdV equation, the discrete LotkaVolterra equation, and the discrete Liouville equation are included. Lax representations of these equations can be used to construct sufficiently many integrals for the reductions. As examples we show that the (3,2) reductions of the integrable partial difference equations are Liouville integrable in their own right.
 Publication:

Regular and Chaotic Dynamics
 Pub Date:
 November 2016
 DOI:
 10.1134/S1560354716060083
 arXiv:
 arXiv:1608.08010
 Bibcode:
 2016RCD....21..682T
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 39A20
 EPrint:
 14 pages, 1 figure