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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