Published March 13, 2005
| public
Journal Article
Lax Pairs for the Ablowitz-Ladik System via Orthogonal Polynomials on the Unit Circle
- Creators
- Nenciu, Irina
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 defined by Cantero, Moral, and Velázquez, and by Simon, respectively, to construct Lax pair representations for this system in the periodic, finite, and infinite settings.
Additional Information
© 2005 Hindawi Publishing Corporation. Received December 14, 2004; Accepted March 13, 2005. Communicated by Percy Deift. The author wishes to thank her advisor, Barry Simon, for his encouragement and advice, and for access to preliminary drafts of his two-volume treatise, [13, 14]. She also thanks Percy Deift for suggesting this problem, and Rowan Killip for his very helpful remarks on preliminary versions of this paper.Additional details
- Eprint ID
- 24920
- Resolver ID
- CaltechAUTHORS:20110817-152444760
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2011-08-18Created from EPrint's datestamp field
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2021-11-09Created from EPrint's last_modified field