Dynamics of excited BPS three-vortices

We analyze the dynamics of Bogomol’nyi-Prasad-Sommerfield three-vortex solutions. First, for unexcited vortices, we study the two-dimensional moduli space of centered vortices with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mrow> <mi>y</mi> <mo stretchy="false">→</mo> <mo>−</mo> <mi>y</mi> </mrow> </math> symmetry, and its metric. We identify the one-dimensional subspaces describing the head-on collisions of equidistant collinear and equilateral triangle configurations, where geodesic motion results in 90° and 60° scattering, respectively. Second, by studying the frequency spectrum of vibrational shape modes along these subspaces, we explain how the force-free, geodesic motion is modified by shape mode excitations into a pattern of chaotic multibounce collisions.