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https://hdl.handle.net/2142/86938
Description
Title
Dispersive Estimates for the Schrodinger Equation
Author(s)
Green, William Robert
Issue Date
2010
Doctoral Committee Chair(s)
Erdogan, M. Burak
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mathematics
Language
eng
Abstract
Finally in Chapter 3 we consider a problem involving the non-linear Schrodinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, iut+dtu xx+u2u=0. We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion management solitons. We prove that the dispersion management solitons decay exponentially in x and in the Fourier transform of x.
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