Elizabethan vortices
arXiv:2301.06191 · doi:10.1088/1361-6544/acddc5
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.
arXiv commentDedicated to Nick Manton on the occasion of his 70th birthday. Some typos from the journal version corrected
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