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In this paper we show that the maximal solutions (Φ∈, A∈) in the Abelian Chern-Simons Higgs model on a 't Hooft type periodic domain converges to (Φ * , A * ) and Φ * is a harmonic map. We also study asymptotic behaviors of the energy density.

Asymptotic limit for condensate solutions in the Abelian Chern-Simons Higgs model II