Non-local Hamiltonian structures and applications to the theory of integrable systems I

2012/10/05 by Alberto De Sole, De Sole, Alberto, Victor G. Kač +2 · 1 citation
Mathematics · Physics and Astronomy · #17B63 (Secondary) #17B69 #17B80 #37K10 (Primary) 35Q53 #37K30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA) #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.1210.1688

55 pages

arxiv created 2012/10/05 · openalex publication_date 2012/10/05 · arxiv updated 2015/12/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We develop a rigorous theory of non-local Hamiltonian structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee applicability of the Lenard-Magri scheme of integrability to a pair of compatible non-local Hamiltonian structures.

Citations

• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory

Cited by

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

Related

• Non-local Poisson structures and applications to the theory of integrable systems II
• Poisson integrators
• Poisson vertex algebras and Hamiltonian PDE
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