Integrable vortices on compact Riemann surfaces of genus one

Abstract

Abstract The Jackiw-Pi equation, which is one of the integrable vortex equations, is studied on a torus, a compact Riemann surface of genus one. The solutions are given in terms of doubly periodic functions, i.e., the elliptic functions. We reconsider the Jackiw-Pi vortex on a torus and provide the analytical method for determining the vortex number with explicit examples.