A Bi-Hamiltonian Theory for Stationary KdV Flows and their Separability

2000/03/09 by Gregorio Falqui, Franco Magri, Falqui, Gregorio +5 · 1 citation
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Magnetic confinement fusion research #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.nlin/0003020

openalex publication_date 2000/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Invariant Reduction for Partial Differential Equations. III: Poisson Brackets

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