Elizabethan vortices
High Energy Physics - Theory
2023-12-19 v3 Differential Geometry
Exactly Solvable and Integrable Systems
Abstract
Radial solutions to the elliptic sinh-Gordon and Tzitzeica equations can be interpreted as Abelian vortices on certain surfaces of revolution. These surfaces have a conical excess angle at infinity (in a way which makes them similar to Elizabethan ruff collars). While they can not be embedded in the Euclidean 3-space, we will show that they can be globally embedded in the hyperbolic space. The existence of these hyperbolic embeddings follows from the asymptotic analysis of a Painleve III ODE.
Keywords
Cite
@article{arxiv.2301.06191,
title = {Elizabethan vortices},
author = {Maciej Dunajski and Nora Gavrea},
journal= {arXiv preprint arXiv:2301.06191},
year = {2023}
}
Comments
Dedicated to Nick Manton on the occasion of his 70th birthday. Some typos from the journal version corrected