Bogomolny equations from the Pseudoanalytic Functions Viewpoint

T. Supatashvili
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Abstract

In the following paper we are going to study a special kind of solitons, called vortices. We will define the topological number for them, called the vortex number. Switching to complex variables and using a different approach from the one used by Jaffe and Taubes in the famous monograph "Vortices and monopoles", 1980, in particular, using the theorems known in pseudoanalytic function theory, we construct the vortex solutions of the field equations for our problem and write out the vortex numbers for them that will be characterized by the zeroes of each possible solution.
伪解析函数视点下的Bogomolny方程
在下一篇文章中,我们将研究一种特殊的孤子,称为涡旋。我们将为它们定义拓扑数,称为涡数。切换到复变量,并使用与Jaffe和Taubes在著名的专著“涡旋和单极子”(1980)中使用的方法不同的方法,特别是使用伪解析函数理论中已知的定理,我们为我们的问题构造了场方程的涡旋解,并写出了它们的涡旋数,这些涡旋数将以每个可能解的零为特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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