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

Citation

Nenciu, Irina (2005) Lax pairs for the Ablowitz-Ladik system via orthogonal polynomials on the unit circle. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05122005-103528

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 Schroedinger 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 Velazquez, and Simon, respectively, to construct Lax pair representations for the Ablowitz-Ladik hierarchy in the periodic, finite, and infinite settings.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:integrable systems; orthogonal polynomials
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Simon, Barry M.
Thesis Committee:
  • Simon, Barry M. (chair)
  • Damanik, David
  • Killip, Rowan
  • Kaloshin, Vadim
Defense Date:9 May 2005
Record Number:CaltechETD:etd-05122005-103528
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05122005-103528
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1750
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:13 May 2005
Last Modified:26 Dec 2012 02:41

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