Contatto F. Vortex-like solitons and Painleve integrability, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract): Difference between revisions
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| title = Vortex-like solitons and Painlevé integrability | | 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. | | 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. | ||
| slides = | | slides = [[Media:Contatto F. Vortex-like solitons and Painleve integrability (presentation at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic).pdf|Contatto F. Vortex-like solitons and Painleve integrability (presentation at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic).pdf]] | ||
| references = | | references = | ||
| 79YY-MM-DD = 7984-89-81 | | 79YY-MM-DD = 7984-89-81 | ||
}} | }} | ||
Latest revision as of 16:45, 23 November 2015
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.