Lax pairs for the Ablowitz-Ladik system via orthogonal polynomials on the unit circle

2004/12/14 by Irina Nenciu, Nenciu, Irina · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.CA #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.math-ph/0412047

38 pages

arxiv created 2004/12/14 · openalex publication_date 2004/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nenciu and Simon found that the analogue of the Toda system in the context of orthogonal polynomials on the unit circle is the defocusing Ablowitz-Ladik system. In this paper we use the CMV and extended CMV matrices, respectively, to construct Lax pair representations for this system in the periodic, finite, and infinite cases.

Cited by

• Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz–Ladik Hierarchy
• Limiting distribution of maximal crossing and nesting of Poissonized random matchings

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