Multivortex solutions in the Chern–Simons gauged [formula omitted] sigma model on a doubly periodic domain

Abstract

We establish the existence and uniqueness results for multivortex solutions of an elliptic equation arising from the self-dual Chern–Simons gauged O(3) sigma model with a symmetric potential on a flat 2-torus. We prove that if the parameter ε>0 is small then the elliptic governing equation admits a maximal solution. We also study the asymptotic behavior of the maximal solutions as ε→0. By using this asymptotic behavior we establish the uniqueness results for solutions which tend to ∞ a.e. as ε→0 under suitable conditions on the Dirac measure.