Contatto F. Vortex-like solitons and Painleve integrability, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)
Speaker: Felipe Contatto
Title: Vortex-like solitons and Painlevé integrability
The Abelian Higgs model admits topological solitons called vortices, which can be considered as finite energy solutions to the Taubes equation. They are static solutions on a two-dimensional Riemannian manifold. This equation is not integrable in general and few exact solutions are known (the most famous one being on hyperbolic surfaces). I will present a modified version of this model that generalises the usual theory and admits vortex-like solitons, then I will study integrability of the modified Taubes equation using Painlevé analysis and derive some exact solutions. Despite being defined on a smooth surface, these solitons have a secondary interpretation as vortices on a conifold. The approach illustrates how Painlevé analysis can be helpful in the construction of topological solitons.
Slides: Contatto F. Vortex-like solitons and Painleve integrability (presentation at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic).pdf