A Bi-Hamiltonian Theory for Stationary KdV Flows and their Separability
Exactly Solvable and Integrable Systems
2009-09-25 v1
Abstract
We present a fairly new and comprehensive approach to the study of stationary flows of the Korteweg-de Vries hierarchy. They are obtained by means of a double restriction process from a dynamical system in an infinite number of variables. This process naturally provides us with a Lax representation of the flows, which is used to find their bi-Hamiltonian formulation. Then we prove the separability of these flows making use of their bi-Hamiltonian structure, and we show that the variables of separation are supplied by the Poisson pair.
Keywords
Cite
@article{arxiv.nlin/0003020,
title = {A Bi-Hamiltonian Theory for Stationary KdV Flows and their Separability},
author = {Gregorio Falqui and Franco Magri and Marco Pedroni and Jorge P. Zubelli},
journal= {arXiv preprint arXiv:nlin/0003020},
year = {2009}
}
Comments
Latex, 21 pages. To appear in Regular and Chaotic Dynamics