Existence Theorems for πn Vortex Scattering
Abstract
The analysis of 90 vortex-vortex scattering is extended to πn scattering in all head-on collisions of n vortices in the Abelian Higgs model. A Cauchy problem with initial data that describe the scattering of n vortices is formulated. It is shown that this Cauchy problem has a unique global finite-energy solution. The symmetry of the solution and the form of the local analytic solution then show that πn scattering is realised.
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