{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/104763"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/104763","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Bifurcations in nonlinear Schrödinger equations with double well potentials","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Kim, Hee Yeon"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Kirr, Eduard Wilhelm","Laugesen, Richard S.","Bronski, Jared C.","Hur, Vera Mikyoung"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-08-23T19:51:33Z","date_published":"2019-08-23T19:51:33Z","updated_at":"2026-07-22T22:24:42Z","subjects":["Schrödinger equation","Bifurcation","Bound states","Double wells"],"languages":["en"],"rights":["Copyright 2019 Hee Yeon Kim"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/104763","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kirr, Eduard Wilhelm","Laugesen, Richard S.","Bronski, Jared C.","Hur, Vera Mikyoung"]},{"key":"dc:creator","label":"Author","values":["Kim, Hee Yeon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-08-23T19:51:33Z","2019-04-02","2019-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Schrödinger equation","Bifurcation","Bound states","Double wells"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Hee Yeon Kim"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/104763"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Submission original under an indefinite embargo labeled 'Open Access'. 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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.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo terms","The student, Hee Yeon Kim, accepted the attached license on 2019-03-22 at 23:53.","The student, Hee Yeon Kim, submitted this Dissertation for approval on 2019-03-23 at 00:04.","This Dissertation was approved for publication on 2019-04-02 at 11:22.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13444 on 2019-08-22 at 14:40:43","Made available in DSpace on 2019-08-23T19:51:33Z (GMT). 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