Title page for ETD etd-06302007-091322


Type of Document Dissertation
Author Keister, Adrian Clark
URN etd-06302007-091322
Title On the Eigenvalues of the Manakov System
Degree PhD
Department Mathematical Physics
Advisory Committee
Advisor Name Title
Klaus, Martin Committee Chair
Day, Martin V. Committee Member
Hagedorn, George A. Committee Member
Jacobs, Ira Committee Member
Kohler, Werner E. Committee Member
Keywords
  • Zakharov-Shabat
  • chirp
  • fiber optics
  • inverse scattering transform
  • soliton
  • coupled nonlinear Schr\"odinger equations
  • nonlinear Schr\"odinger equation
  • Manakov
Date of Defense 2007-06-26
Availability unrestricted
Abstract
We clear up two issues regarding the eigenvalue problem for the Manakov system; these problems relate directly to the existence of the soliton [\emph{sic}] effect in fiber optic cables.

The first issue is a bound on the eigenvalues of the Manakov system: \emph{if} the parameter $\xi$ is an eigenvalue, \emph{then} it must lie in a certain region in the complex plane.

The second issue has to do with a chirped Manakov system.

We show that if a system is chirped too much, the soliton effect disappears.

While this has been known for some time experimentally, there has not yet been a theoretical result along these lines for the Manakov system.

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