Generalised point vortices on a plane

Abstract

A three-vortex system on a plane is known to be minimally superintegrable in the Liouville sense. In this work, integrable generalisations of the three-vortex planar model, which involve root vectors of simple Lie algebras, are proposed. It is shown that a generalised system, which is governed by a positive definite Hamiltonian, admits a natural integrable extension by spin degrees of freedom. It is emphasised that the n-vortex planar model and plenty of its generalisations enjoy the nonrelativistic scale invariance, which gives room for possible holographic applications.

arXiv comment11 pages

References in corpus (4)

• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Lie algebras in vortex dynamics and celestial mechanics - IV
• Remarks on N=1 supersymmetric extension of the Euler top
• Integrability of point-vortex dynamics via symplectic reduction: a survey

Cited by in corpus (3)

• Equations of fluid dynamics with the l-conformal Galilei symmetry
• Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
• Phase portraits and the bifurcation set for the three-vortex interaction system