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

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.

arXiv comment38 pages

Cited by in corpus (6)

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• Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials
• Darboux transformations for CMV matrices
• The Ablowitz-Ladik Hierarchy Revisited