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Type of Document	Dissertation
Author	Nenciu, Irina
URN	etd-05122005-103528
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-05122005-103528
Title	Lax pairs for the Ablowitz-Ladik system via orthogonal polynomials on the unit circle
Degree	PhD
Option	Mathematics
Advisory Committee	Advisor Name Title Barry Simon Committee Chair David Damanik Committee Member Rowan Killip Committee Member Vadim Kaloshin Committee Member
Keywords	orthogonal polynomials integrable systems
Date of Defense	2005-05-09
Availability	unrestricted
Abstract We investigate the existence and properties of an integrable system related to orthogonal polynomials on the unit circle. We prove that the main evolution of the system is defocusing Ablowitz-Ladik (also known as the integrable discrete nonlinear Schröedinger equation). In particular, we give a new proof of complete integrability for this system. Furthermore, we use the CMV and extended CMV matrices defined in the context of orthogonal polynomials on the unit circle by Cantero, Moral, and Velázquez, and Simon, respectively, to construct Lax pair representations for the Ablowitz-Ladik hierarchy in the periodic, finite, and infinite settings.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    cv-Nenciu.pdf 54.20 Kb 00:00:15 00:00:07 00:00:06 00:00:03 < 00:00:01   Thesis.pdf 417.30 Kb 00:01:55 00:00:59 00:00:52 00:00:26 00:00:02