scientific article; zbMATH DE number 2188797

DOI10.1155/IMRN.2005.647zbMath1081.37047arXivmath-ph/0412047MaRDI QIDQ5461859

Irina Nenciu

Publication date: 27 July 2005

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0412047

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

orthogonal polynomialsHamiltoniansLax pairsAblowitz-Ladik hierarchyAblowitz-Ladik lattice

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Lattice dynamics; integrable lattice equations (37K60)

Related Items

Hydrodynamic equations for the Ablowitz–Ladik discretization of the nonlinear Schrödinger equation ⋮ Darboux transformations for CMV matrices ⋮ Weyl--Titchmarsh theory for CMV operators associated with orthogonal polynomials on the unit circle ⋮ A generalization of Laurent biorthogonal polynomials and related integrable lattices ⋮ DSF chain for biorthogonal polynomials and its application to matrix eigenvalue problems ⋮ Orthogonal polynomials, Toda lattices and Painlevé equations ⋮ CMV matrices: Five years after ⋮ Modulational instability and position controllable discrete rogue waves with interaction phenomena in the semi-discrete complex coupled dispersionless system ⋮ Orthogonal Laurent polynomials on the unit circle, extended CMV ordering and 2D Toda type integrable hierarchies ⋮ Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials ⋮ Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular \(\beta\)-ensemble and double confluent Heun equation ⋮ Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems ⋮ Conversations with Flaschka: Kac-Moody groups and Verblunsky coefficients ⋮ Large deviations for Ablowitz-Ladik lattice, and the Schur flow ⋮ Limiting distribution of maximal crossing and nesting of Poissonized random matchings ⋮ A note on Poisson brackets for orthogonal polynomials on the unit circle ⋮ OPUC on one foot ⋮ Microscopic conservation laws for integrable lattice models ⋮ Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz–Ladik Hierarchy ⋮ The periodic defocusing Ablowitz-Ladik equation and the geometry of Floquet CMV matrices ⋮ Trace formulas and a Borg‐type theorem for CMV operators with matrix‐valued coefficients ⋮ Poisson brackets of orthogonal polynomials ⋮ Multi‐Hamiltonian structure for the finite defocusing Ablowitz‐Ladik equation ⋮ Extended relativistic Toda lattice, L-orthogonal polynomials and associated Lax pair ⋮ Algebro-geometric solutions of the Baxter-Szegő difference equation ⋮ Discrete integrable systems and random Lax matrices ⋮ Nonisospectral extension of Schur flow with determinant solution and orthogonal polynomials on the unit circle