In this work, we investigate the solutions of vortices in the O(3)-sigma model with the gauge field governed by the Chern-Simons term and subject to a hyperbolic self-dual potential. We show that this model admits both topological and nontopological solitons solutions. By means of numerical analysis, we realize that the topological solutions of the model can be transformed into compacton-like solutions. On the other hand, after modifying the model by the introduction of a dielectric constant, an interesting feature appears; namely, the nontopological solutions can be transformed into kink-like solutions through the numerical variation of the dielectric constant. Finally, we discuss the degeneracy for the topological solitons in a given sector and present the numerical solutions of the first model.

中文翻译：

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在 O(3)-sigma 模型中将扭结转化为压缩

在这项工作中，我们研究了 O(3)-sigma 模型中涡旋的解，其中规范场由 Chern-Simons 项控制，并受双曲自对偶势的影响。我们表明该模型允许拓扑和非拓扑孤子解决方案。通过数值分析，我们认识到模型的拓扑解可以转化为compacton-like解。另一方面，通过引入介电常数修改模型后，出现了一个有趣的特征；即非拓扑解可以通过介电常数的数值变化转化为类扭结解。最后，我们讨论了给定扇区中拓扑孤子的简并性，并给出了第一个模型的数值解。