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Title:Bifurcations in nonlinear Schrödinger equations with double well potentials
Author(s):Kim, Hee Yeon
Director of Research:Kirr, Eduard Wilhelm
Doctoral Committee Chair(s):Laugesen, Richard S.
Doctoral Committee Member(s):Bronski, Jared C.; Hur, Vera Mikyoung
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Schrödinger equation
Bifurcation
Bound states
Double wells
Abstract:In this thesis, we consider nonlinear Schrödinger equations with double well potentials with attractive and repelling nonlinearities. We discuss bifurcations along bound states, especially ground states and the first excited states, and also deal with orbital stability of the ground states. In attractive case with large separations for double wells, our results shows that the ground state must undergo the secondary symmetry breaking bifurcation, while the first excited states can be uniquely extended as long as the bifurcation of the ground state has not occurred. In repelling case with large separations for double wells, we prove that the secondary bifurcation of the ground state does not emerge, even in the strongly nonlinear regime, while the first excited state must undergo the secondary bifurcation on the first excited states.
Issue Date:2019-04-02
Type:Text
URI:http://hdl.handle.net/2142/104763
Rights Information:Copyright 2019 Hee Yeon Kim
Date Available in IDEALS:2019-08-23
Date Deposited:2019-05


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