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Asymptotic stability and completeness in 2D nonlinear Schrodinger equation

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Title: Asymptotic stability and completeness in 2D nonlinear Schrodinger equation
Author(s): Skulkhu, Ruth
Director of Research: Kirr, Eduard-Wilhelm
Doctoral Committee Chair(s): Bronski, Jared C.
Doctoral Committee Member(s): Zharnitsky, Vadim; Kirr, Eduard-Wilhelm; Laugesen, Richard S.
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Mathematics Partial Differential Equations Schrödinger Equation Nonlinear Completeness Asymptotic Stability
Abstract: In this thesis we obtained new results on the asymptotic stability of ground states of the nonlinear Schrödinger equation in space dimension two. Under our hypotheses, the result actually shows asymptotic completeness in the regime of small initial data, i.e. any small initial data evolves into a superposition of a solitary wave (ground state) and a radiative part that decays in time.
Issue Date: 2012-06-27
URI: http://hdl.handle.net/2142/32082
Rights Information: © 2012 by Ruth J. Skulkhu. All rights reserved.
Date Available in IDEALS: 2012-06-27
Date Deposited: 2012-05
 

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