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Zero modes and degrees of freedom of topological solitons on the plane
Includes bibliographical references.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2015
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| _version_ | 1867613181238575104 |
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| access_status_str | Open Access |
| author | Adams, Rory Montague |
| author2 | Barashenkov, I V |
| author_browse | Adams, Rory Montague Barashenkov, I V |
| author_facet | Barashenkov, I V Adams, Rory Montague |
| author_sort | Adams, Rory Montague |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/13891 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:03.909Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/13891 Zero modes and degrees of freedom of topological solitons on the plane Adams, Rory Montague Barashenkov, I V Mathematics and Applied Mathematics Includes bibliographical references. 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. 2015-09-14T18:05:20Z 2015-09-14T18:05:20Z 2003 Master Thesis Masters MSc http://hdl.handle.net/11427/13891 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Adams, Rory Montague Zero modes and degrees of freedom of topological solitons on the plane |
| thesis_degree_str | Master's |
| title | Zero modes and degrees of freedom of topological solitons on the plane |
| title_full | Zero modes and degrees of freedom of topological solitons on the plane |
| title_fullStr | Zero modes and degrees of freedom of topological solitons on the plane |
| title_full_unstemmed | Zero modes and degrees of freedom of topological solitons on the plane |
| title_short | Zero modes and degrees of freedom of topological solitons on the plane |
| title_sort | zero modes and degrees of freedom of topological solitons on the plane |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/13891 |
| work_keys_str_mv | AT adamsrorymontague zeromodesanddegreesoffreedomoftopologicalsolitonsontheplane |