Nenciu, Irina (2005) Lax Pairs for the Ablowitz-Ladik System via Orthogonal Polynomials on the Unit Circle. International Mathematics Research Notices, 2005 (11). pp. 647-686. ISSN 1073-7928. http://resolver.caltech.edu/CaltechAUTHORS:20110817-152444760
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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.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Jason Perez|
|Deposited On:||18 Aug 2011 18:28|
|Last Modified:||18 Aug 2011 18:31|
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