{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/13891"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/13891","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Zero modes and degrees of freedom of topological solitons on the plane","abstract":"In this thesis we analyse the coaxial multivortices of the Ginzburg-Landau, the Euclidean complex sine-Gordon-1 and -2 theories on the plane. More specifically, we determine the number of continuous free parameters describing the largest family of solutions, with these vortices as members. This is accomplished by obtaining the zero modes of the vortices. For the Ginzburg-Landau model we show that the multivortices do not belong to a larger family of solutions and only depend on parameters describing their global U(1) symmetry and translations in the plane. Thus it is not possible to continuously deform these coaxial multivortices into a system of multiple, separated vortices. In contrast, the multivortices of complex sine-Gordon-1 model are shown to have an infinite number of zero modes and can be continuously deformed into a configuration of multiple, separated vortices. We also show that the largest family of solutions, with these coaxial multivortices as members, is a recently discovered family describing non-coaxial multivortices. For the complex sine-Gordon-2, we show the coaxial multivortices belong to a larger family of solutions which depend on a finite number of continuous free parameters. We also speculate as to the form of solutions that this larger family can describe.","abstract_html":"In this thesis we analyse the coaxial multivortices of the Ginzburg-Landau, the Euclidean complex sine-Gordon-1 and -2 theories on the plane. More specifically, we determine the number of continuous free parameters describing the largest family of solutions, with these vortices as members. This is accomplished by obtaining the zero modes of the vortices. For the Ginzburg-Landau model we show that the multivortices do not belong to a larger family of solutions and only depend on parameters describing their global U(1) symmetry and translations in the plane. Thus it is not possible to continuously deform these coaxial multivortices into a system of multiple, separated vortices. In contrast, the multivortices of complex sine-Gordon-1 model are shown to have an infinite number of zero modes and can be continuously deformed into a configuration of multiple, separated vortices. We also show that the largest family of solutions, with these coaxial multivortices as members, is a recently discovered family describing non-coaxial multivortices. For the complex sine-Gordon-2, we show the coaxial multivortices belong to a larger family of solutions which depend on a finite number of continuous free parameters. We also speculate as to the form of solutions that this larger family can describe.","abstract_has_math":false,"creators":["Adams, Rory Montague"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Barashenkov, I V"],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003","date_published":"2003","updated_at":"2026-07-22T22:22:43Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/13891","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Barashenkov, I V"]},{"key":"dc:creator","label":"Author","values":["Adams, Rory Montague"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-09-14T18:05:20Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-09-14T18:05:20Z"]},{"key":"dc:date.issued","label":"Date","values":["2003"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/13891"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliographical references."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we analyse the coaxial multivortices of the Ginzburg-Landau, the Euclidean complex sine-Gordon-1 and -2 theories on the plane. More specifically, we determine the number of continuous free parameters describing the largest family of solutions, with these vortices as members. This is accomplished by obtaining the zero modes of the vortices. For the Ginzburg-Landau model we show that the multivortices do not belong to a larger family of solutions and only depend on parameters describing their global U(1) symmetry and translations in the plane. Thus it is not possible to continuously deform these coaxial multivortices into a system of multiple, separated vortices. In contrast, the multivortices of complex sine-Gordon-1 model are shown to have an infinite number of zero modes and can be continuously deformed into a configuration of multiple, separated vortices. We also show that the largest family of solutions, with these coaxial multivortices as members, is a recently discovered family describing non-coaxial multivortices. For the complex sine-Gordon-2, we show the coaxial multivortices belong to a larger family of solutions which depend on a finite number of continuous free parameters. We also speculate as to the form of solutions that this larger family can describe."]},{"key":"dc:title","label":"Title","values":["Zero modes and degrees of freedom of topological solitons on the plane"]}]}],"canonical_facts":{"dc:contributor.advisor":["Barashenkov, I V"],"dc:creator":["Adams, Rory Montague"],"dc:date.accessioned":["2015-09-14T18:05:20Z"],"dc:date.available":["2015-09-14T18:05:20Z"],"dc:date.issued":["2003"],"dc:description":["Includes bibliographical references."],"dc:description.abstract":["In this thesis we analyse the coaxial multivortices of the Ginzburg-Landau, the Euclidean complex sine-Gordon-1 and -2 theories on the plane. More specifically, we determine the number of continuous free parameters describing the largest family of solutions, with these vortices as members. This is accomplished by obtaining the zero modes of the vortices. For the Ginzburg-Landau model we show that the multivortices do not belong to a larger family of solutions and only depend on parameters describing their global U(1) symmetry and translations in the plane. Thus it is not possible to continuously deform these coaxial multivortices into a system of multiple, separated vortices. In contrast, the multivortices of complex sine-Gordon-1 model are shown to have an infinite number of zero modes and can be continuously deformed into a configuration of multiple, separated vortices. We also show that the largest family of solutions, with these coaxial multivortices as members, is a recently discovered family describing non-coaxial multivortices. For the complex sine-Gordon-2, we show the coaxial multivortices belong to a larger family of solutions which depend on a finite number of continuous free parameters. We also speculate as to the form of solutions that this larger family can describe."],"dc:identifier.uri":["http://hdl.handle.net/11427/13891"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Zero modes and degrees of freedom of topological solitons on the plane"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:43Z"}