TL;DR
This paper explores the dynamics of periodic monopoles by numerically constructing solutions that model monopole collisions and scattering, revealing insights into their slow-motion evolution and interactions.
Contribution
It introduces a numerical method to construct a family of Hitchin equation solutions representing monopole dynamics on a cylinder, linking monopole scattering to geodesic motion.
Findings
Monopole chains collide and scatter at right angles.
A one-parameter family of solutions models slow-motion monopole evolution.
Numerical solutions illustrate monopole interactions on a cylindrical geometry.
Abstract
BPS monopoles which are periodic in one of the spatial directions correspond, via a generalized Nahm transform, to solutions of the Hitchin equations on a cylinder. A one-parameter family of solutions of these equations, representing a geodesic in the 2-monopole moduli space, is constructed numerically. It corresponds to a slow-motion dynamical evolution, in which two parallel monopole chains collide and scatter at right angles.
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