Multi‐Hamiltonian structure for the finite defocusing Ablowitz‐Ladik equation

DOI10.1002/cpa.20255zbMath1153.37410arXiv0706.2428OpenAlexW2963038276MaRDI QIDQ5503314

Irina Nenciu, Michael I. Gekhtman

Publication date: 13 January 2009

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.2428

Mathematics Subject Classification ID

Related Items (6)

Darboux transformations for CMV matrices ⋮ Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular \(\beta\)-ensemble and double confluent Heun equation ⋮ Large deviations for Ablowitz-Ladik lattice, and the Schur flow ⋮ A note on Poisson brackets for orthogonal polynomials on the unit circle ⋮ Poisson brackets of orthogonal polynomials ⋮ Discrete integrable systems and random Lax matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lie algebraic aspects of the finite nonperiodic Toda flows
• Zeros of OPUC and long time asymptotics of Schur and related flows
• Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices
• The solution to a generalized Toda lattice and representation theory
• Poisson geometry of the analog of the Miura maps and Bäcklund-Darboux transformations for equations of Toda type and periodic Toda flows
• Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
• The toda flow on a generic orbit is integrable
• Nonlinear differential−difference equations
• Nonlinear differential–difference equations and Fourier analysis
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• NonAbelian nonlinear lattice equations on finite interval
• The Toda lattice. II. Existence of integrals
• On Schur flows
• A family of the Poisson brackets compatible with the Sklyanin bracket
• CMV: The unitary analogue of Jacobi matrices

This page was built for publication: Multi‐Hamiltonian structure for the finite defocusing Ablowitz‐Ladik equation