{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/11261"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/11261","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Spectral continuation study of the temporally periodic solitons of the damped-driven nonlinear Schrödinger equations","abstract":"In this thesis we develop and employ a spectral continuation algorithm, implemented in AUTO, to study the temporally periodic spatially localised soliton solutions of the driven, damped nonlinear Schrödinger equations, both in the case of parametric driving and direct driving. We hope that this study is of interest not only in the context of the nonlinear Schrödinger equations but also separately as a study of an efficient numerical algorithm for continuing (path-following) solutions to general two-dimensional periodic soliton bearing PDEs.","abstract_html":"In this thesis we develop and employ a spectral continuation algorithm, implemented in AUTO, to study the temporally periodic spatially localised soliton solutions of the driven, damped nonlinear Schrödinger equations, both in the case of parametric driving and direct driving. We hope that this study is of interest not only in the context of the nonlinear Schrödinger equations but also separately as a study of an efficient numerical algorithm for continuing (path-following) solutions to general two-dimensional periodic soliton bearing PDEs.","abstract_has_math":false,"creators":["Lee-Thorpe, James"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Barashenkov, Igor"],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-22T22:23:19Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/11261","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Barashenkov, Igor"]},{"key":"dc:creator","label":"Author","values":["Lee-Thorpe, James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-01-04T14:29:31Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-01-04T14:29:31Z"]},{"key":"dc:date.issued","label":"Date","values":["2012"]},{"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/11427/11261"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes abstract.","Includes bibliographical references."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we develop and employ a spectral continuation algorithm, implemented in AUTO, to study the temporally periodic spatially localised soliton solutions of the driven, damped nonlinear Schrödinger equations, both in the case of parametric driving and direct driving. We hope that this study is of interest not only in the context of the nonlinear Schrödinger equations but also separately as a study of an efficient numerical algorithm for continuing (path-following) solutions to general two-dimensional periodic soliton bearing PDEs."]},{"key":"dc:title","label":"Title","values":["Spectral continuation study of the temporally periodic solitons of the damped-driven nonlinear Schrödinger equations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Barashenkov, Igor"],"dc:creator":["Lee-Thorpe, James"],"dc:date.accessioned":["2015-01-04T14:29:31Z"],"dc:date.available":["2015-01-04T14:29:31Z"],"dc:date.issued":["2012"],"dc:description":["Includes abstract.","Includes bibliographical references."],"dc:description.abstract":["In this thesis we develop and employ a spectral continuation algorithm, implemented in AUTO, to study the temporally periodic spatially localised soliton solutions of the driven, damped nonlinear Schrödinger equations, both in the case of parametric driving and direct driving. 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