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
Abstract:
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.