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Self-Dual Symmetric Nontopological Solutions in the SU(3) Model in \({\mathbb{R}^2}\)

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Abstract

In this paper, we study non-topological solutions (u 1, u 2) to the SU(3) Chern–Simons system, satisfying the asymptotic behavior \({u_k(x)=-2\alpha_k\ln |x|+O(1)}\) for some \({\alpha_k > 1, k = 1, 2}\). We show that solutions remain uniformly bounded as long as (α 1, α 2) lies in S N (see Sect. 1), and then we prove the existence of non-topological solutions for any \({(\alpha_1,\alpha_2)\in S_N}\). For this purpose, we have to study the phenomena of partial blowup at infinity, and show that S N is the optimal range of (α 1, α 2) such that the partial blowup could occur if (α 1, α 2) is on some part of \({\partial S_N}\).

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Authors and Affiliations

  1. Department of Mathematics, Inha University, Incheon, 402-751, Republic of Korea

    Kwangseok Choe

  2. Department of Mathematics, Chosun University, Kwangju, 501-759, Republic of Korea

    Namkwon Kim

  3. Department of Mathematics, Taida Institute for Mathematical Sciences (TIMS), National Taiwan University, Taipei, Taiwan

    Chang-Shou Lin

Authors
  1. Kwangseok Choe
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  2. Namkwon Kim
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  3. Chang-Shou Lin
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Correspondence to Namkwon Kim.

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Communicated by H.-T. Yau

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Choe, K., Kim, N. & Lin, CS. Self-Dual Symmetric Nontopological Solutions in the SU(3) Model in \({\mathbb{R}^2}\) . Commun. Math. Phys. 334, 1–37 (2015). https://doi.org/10.1007/s00220-014-2109-7

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