We study condensate solutions of a nonlinear elliptic equation in ℝ2, which models a W-boson with a cosmic string background. The existence of condensate solutions and an energy identity are discussed, based on which the refined asymptotic behavior of condensate solutions is established by studying the corresponding evolution dynamical system. Applying the "shrinking-sphere" method, we also prove the symmetry under inversions of condensate solutions for some special cases.
Bibliographical noteFunding Information:
∗R. M. C. was supported in part by NSF grant no. DMS-0908663. †D. S. was supported in part by NSF grant no. DMS-0707714 and NSF grant no. DMS-0955687.