In this paper, we first introduce the first-order formalism with the self-dual structure of the motion equations, also called the Bogomol’nyi and Prasad–Sommerfield (BPS) equations. We observe that BPS equations arising in the generalized Maxwell–Higgs model under specific circumstances can be transformed into a vortices–antivortices equation, which is a nonlinear elliptic equation with the exponential functions. For the vortices–antivortices equation in two space dimensions, we prove the existence of topological solutions by a monotone iteration method. Finally, we give the asymptotic estimates of solutions obtained at infinity.

中文翻译：

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涡-反涡方程中拓扑解的存在性

在本文中，我们首先介绍了具有自对偶结构的运动方程的一阶形式，也称为 Bogomol'nyi 和 Prasad-Sommerfield (BPS) 方程。我们观察到广义麦克斯韦-希格斯模型在特定情况下产生的BPS方程可以转化为涡旋-反涡旋方程，这是一个具有指数函数的非线性椭圆方程。对于二维空间的涡-反涡方程，我们用单调迭代法证明了拓扑解的存在性。最后，我们给出了在无穷远处获得的解的渐近估计。