Via degli Arcimboldi 8, I - 20126 Milano, Italy
Dipartimento di Matematica e Applicazioni Universit`a di Milano-Bicocca
Falqui G. G., Magri F., Pedroni M., Zubelli J. P.
A Bi-Hamiltonian Theory for Stationary KDV Flows and Their Separability
2000, vol. 5, no. 1, pp. 33-52
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.