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 Uniqueness of topological solutions for the Gudnason Model J. Korean Math. Soc.Published online December 2, 2020 Soojung Kim and Youngae Lee Soongsil University, Kyungpook National University Abstract : In this paper, we consider the Gudnason model of $\mathcal{N} = 2$ supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime. Keywords : elliptic system; topological solution; uniqueness; linearized operator MSC numbers : 35A02; 35B45; 35J47;35B20;35Q60 Full-Text :