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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>y</a:mi><a:mo stretchy="false">→</a:mo><a:mo>−</a:mo><a:mi>y</a:mi></a:mrow></a: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.