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. © Regular and Chaotic Dynamics.
Falqui, G., Magri, F., Pedroni, M., Zubelli, J. (2000). A bi-Hamiltonian theory for stationary KdV flows and their separability. REGULAR & CHAOTIC DYNAMICS, 5(1), 33-52 [10.1070/RD2000v005n01ABEH000122].
A bi-Hamiltonian theory for stationary KdV flows and their separability
FALQUI, GREGORIO;MAGRI, FRANCO;
2000
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. © Regular and Chaotic Dynamics.
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