Bifurcations in nonlinear Schrödinger equations with double well potentials

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Kim, Hee Yeon

Contributors dc:contributor

• Kirr, Eduard Wilhelm
• Laugesen, Richard S.
• Bronski, Jared C.
• Hur, Vera Mikyoung

• Schrödinger equation
• Bifurcation
• Bound states
• Double wells

Statement dc:rights

• Copyright 2019 Hee Yeon Kim

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/104763

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/104763