Title: Cosmic strings in a generalized linear formulation of gauge field theory Show Chinese title

Title: 广义线性规范场理论中的宇宙弦

Abstract: In this note we construct self-dual cosmic strings from a gauge field theory with a generalized linear formation of potential energy density. By integrating the Einstein equation, we obtain a nonlinear elliptic equation which is equal with the sources. We prove the existence of a solution in the broken symmetry category on the full plane and the multiple string solutions are valid under a sufficient condition imposed only on the total string number N. The technique of upper-lower solutions and the method of regularization are employed to show the existence of a solution when there are at least two distant string centers. When all the string centers are identical, fixed point theorem are used to study the properties of the nonlinear elliptic equation. Finally, We give the sharp asymptotic estimate for the solution at infinity. Show Chinese abstract

Abstract: 在本文中，我们从具有广义线性势能密度形式的规范场论中构造自对偶宇宙弦。通过积分爱因斯坦方程，我们得到一个与源项相等的非线性椭圆方程。我们在整个平面上的破缺对称性类别中证明了解的存在性，且多个弦解在仅对总弦数N施加充分条件时有效。当至少有两个遥远的弦中心时，采用上下解技术和正则化方法来证明解的存在性。当所有弦中心相同时，使用不动点定理来研究非线性椭圆方程的性质。最后，我们给出了解在无穷远处的精确渐近估计。