Non-local Poisson structures and applications to the theory of integrable systems II

2012/11/11 by Alberto De Sole, De Sole, Alberto, Victor G. Kač +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Nonlinear Waves and Solitons #math-ph #math.MP #math.RA #math.RT #msc:17B63 #msc:17B69 #msc:17B80 #msc:35Q53 #msc:37K10 #msc:37K30

paper · pdf · doi:10.48550/arxiv.1211.2391

55 pages

arxiv created 2012/11/11 · arxiv updated 2015/12/18

Abstract

We develop further the Lenard-Magri scheme of integrability for a pair of compatible non-local Poisson structures, which we discussed in Part I. We apply this scheme to several such pairs, proving thereby integrability of various evolution equations, as well as hyperbolic equations. Some of these equations may be new.

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• Non-local Poisson structures and applications to the theory of integrable systems

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