We investigate the presence of vortex structures in a Maxwell model with a logarithmic generalization. This generalization becomes important because it generates stationary field solutions in models that describe the dynamics of a scalar field. In this work, we will choose to investigate the dynamics of the complex scalar field with the gauge field governed by the Maxwell term. For this, we will investigate the Bogomol'nyi equations to describe the static field configurations. Then, we show numerically that the complex scalar field solutions that generate minimum energy configurations have internal structures. Finally, assuming a planar vision, the magnetic field and the density energy show the interesting feature of the ring-like vortex.

中文翻译：

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对数广义麦克斯韦理论中的环状涡

我们用对数概括研究了麦克斯韦模型中涡旋结构的存在。这种概括很重要，因为它会在描述标量场动力学的模型中生成平稳场解。在这项工作中，我们将选择研究由Maxwell项控制的标量场的复杂标量场的动力学。为此，我们将研究Bogomol'nyi方程来描述静态场配置。然后，我们通过数值显示产生最小能量配置的复杂标量场解具有内部结构。最后，假设具有平面视觉，则磁场和密度能显示出环形涡旋的有趣特征。