{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-2150"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-2150","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"Radial, vortex, and spiral solutions to the nonlinear Schrödinger equation and other reaction--diffusion systems","abstract":"This dissertation explores various solutions to nonlinear reaction-diffusion systems, focusing primarily on the nonlinear Schrödinger equation. Three types of solutions are investigated: radial solutions (with no angular dependence), vortex solutions (with angular dependence but no radial phase dependence), and spiral solutions (which have radial phase dependence). The study considers free particles without potential and trapped particles inside the cylindrical potential with an impenetrable barrier. We show that spiral solutions to the nonlinear Schrödinger equation only exist for a radially constant phase by considering a related system of nonlinear ordinary differential equations. This system is shown to be a special case of the $\\lambda$-$\\omega$ reaction-diffusion system, whose spiral solutions exist for a nonconstant phase.","abstract_html":"This dissertation explores various solutions to nonlinear reaction-diffusion systems, focusing primarily on the nonlinear Schrödinger equation. Three types of solutions are investigated: radial solutions (with no angular dependence), vortex solutions (with angular dependence but no radial phase dependence), and spiral solutions (which have radial phase dependence). The study considers free particles without potential and trapped particles inside the cylindrical potential with an impenetrable barrier. We show that spiral solutions to the nonlinear Schrödinger equation only exist for a radially constant phase by considering a related system of nonlinear ordinary differential equations. This system is shown to be a special case of the $\\lambda$-<span class=\"etd-inline-math\">&omega;</span> reaction-diffusion system, whose spiral solutions exist for a nonconstant phase.","abstract_has_math":true,"creators":["Cummins, James Redmon"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Cox, Christopher","Belinskiy, Boris; Nichols, Roger; Kong, Lingju","College of Engineering and Computer Science"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:47:21Z","subjects":["Differential equations, Nonlinear--Numerical solutions","Gross-Pitaevskii equations","Reaction-diffusion equations"],"languages":["English","eng"],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/972","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Cox, Christopher","Belinskiy, Boris; Nichols, Roger; Kong, Lingju","College of Engineering and Computer Science"]},{"key":"dc:creator","label":"Author","values":["Cummins, James Redmon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-12-01T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral dissertations","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Differential equations, Nonlinear--Numerical solutions","Gross-Pitaevskii equations","Reaction-diffusion equations"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/972"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Mathematics","Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy."]},{"key":"dc:description.abstract","label":"Abstract","values":["This dissertation explores various solutions to nonlinear reaction-diffusion systems, focusing primarily on the nonlinear Schrödinger equation. Three types of solutions are investigated: radial solutions (with no angular dependence), vortex solutions (with angular dependence but no radial phase dependence), and spiral solutions (which have radial phase dependence). The study considers free particles without potential and trapped particles inside the cylindrical potential with an impenetrable barrier. We show that spiral solutions to the nonlinear Schrödinger equation only exist for a radially constant phase by considering a related system of nonlinear ordinary differential equations. This system is shown to be a special case of the $\\lambda$-$\\omega$ reaction-diffusion system, whose spiral solutions exist for a nonconstant phase."]},{"key":"dc:title","label":"Title","values":["Radial, vortex, and spiral solutions to the nonlinear Schrödinger equation and other reaction--diffusion systems"]}]}],"canonical_facts":{"dc:contributor":["Cox, Christopher","Belinskiy, Boris; Nichols, Roger; Kong, Lingju","College of Engineering and Computer Science"],"dc:creator":["Cummins, James Redmon"],"dc:date":["2024-12-01T08:00:00Z"],"dc:description":["Dept. of Mathematics","Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy."],"dc:description.abstract":["This dissertation explores various solutions to nonlinear reaction-diffusion systems, focusing primarily on the nonlinear Schrödinger equation. Three types of solutions are investigated: radial solutions (with no angular dependence), vortex solutions (with angular dependence but no radial phase dependence), and spiral solutions (which have radial phase dependence). The study considers free particles without potential and trapped particles inside the cylindrical potential with an impenetrable barrier. We show that spiral solutions to the nonlinear Schrödinger equation only exist for a radially constant phase by considering a related system of nonlinear ordinary differential equations. This system is shown to be a special case of the $\\lambda$-$\\omega$ reaction-diffusion system, whose spiral solutions exist for a nonconstant phase."],"dc:identifier":["https://scholar.utc.edu/theses/972"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Differential equations, Nonlinear--Numerical solutions","Gross-Pitaevskii equations","Reaction-diffusion equations"],"dc:title":["Radial, vortex, and spiral solutions to the nonlinear Schrödinger equation and other reaction--diffusion systems"],"dc:type":["Doctoral dissertations","Text"]},"updated_at":"2026-07-24T05:47:21Z"}