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Bifurcations in nonlinear Schrödinger equations with double well potentials
Kim, Hee Yeon
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https://hdl.handle.net/2142/104763
Description
- Title
- Bifurcations in nonlinear Schrödinger equations with double well potentials
- Author(s)
- Kim, Hee Yeon
- Issue Date
- 2019-04-02
- Director of Research (if dissertation) or Advisor (if thesis)
- Kirr, Eduard Wilhelm
- Doctoral Committee Chair(s)
- Laugesen, Richard S.
- Committee Member(s)
- Bronski, Jared C.
- Hur, Vera Mikyoung
- Department of Study
- Mathematics
- Discipline
- Mathematics
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Date of Ingest
- 2019-08-23T19:51:33Z
- Keyword(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.
- Graduation Semester
- 2019-05
- Type of Resource
- text
- Permalink
- http://hdl.handle.net/2142/104763
- Copyright and License Information
- Copyright 2019 Hee Yeon Kim
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