Existence of Solutions to the Seiberg-Witten Vortex Equations with Exponential Decay on the Plane

Clifford Taubes showed that the moduli space of the variational equation of the Yang-Mills-Higgs functional on the plane is non-empty, and its elements correspond to “vortices”. Inspired by this result, in this paper, we show that the moduli space of the Hitchin-type dimensional reduction of the Seiberg-Witten equations on the plane contains both exponentially decayed solutions and polynomial growth solutions.