COCKBURN, ALEXANDER,HUGH (2015) Aspects of Vortices and Hyperbolic Monopoles. Doctoral thesis, Durham University.
|PDF - Accepted Version|
This thesis discusses BPS monopoles in hyperbolic space and BPS vortices in the presence of magnetic impurities. We prove explicit formulae for the spectral curve and rational map of a JNR-type hyperbolic monopole, and we use these to study some Platonic examples as well as some new 1-parameter families analogous to Euclidean monopole scattering. Explicit fields and Braam-Austin data for axial hyperbolic monopoles of a particular mass are derived using a correspondence to 1-monopoles, and this data is deformed to give new 1-parameter families.
Numerical techniques are used to study the effect of magnetic impurities on vortices on a flat background. Analytic results for vortices with magnetic impurities are found by adapting previous results on vortices on the hyperbolic plane and the 2-sphere.
|Item Type:||Thesis (Doctoral)|
|Award:||Doctor of Philosophy|
|Keywords:||solitons, monopoles, vortices|
|Faculty and Department:||Faculty of Science > Mathematical Sciences, Department of|
|Copyright:||Copyright of this thesis is held by the author|
|Deposited On:||03 Jun 2015 10:51|