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

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

2004-12-14

arxiv.org/abs/math-ph/0412047v1

Physics

Mathematical Physics

38 pages

Scientific paper

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.

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