Classification of String Solutions for the Self-Dual Einstein–Maxwell–Higgs Model
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In this paper, we are concerned with an elliptic system arising from the Einstein–Maxwell–Higgs model which describes electromagnetic dynamics coupled with gravitational fields in spacetime. Reducing this system to a single equation and setting up the radial ansatz, we classify solutions into three cases: topological solutions, nontopological solutions of type I, and nontopological solutions of type II. There are two important constants: \(a>0\) representing the gravitational constant and \(N\ge 0\) representing the total string number. When \(0\le aN<2\), we give a complete classification of all possible solutions and prove the uniqueness of solutions for a given decay rate. In particular, we obtain a new class of topological solitons, with nonstandard asymptotic value \(\sigma <0\) at infinity, when the total string number is sufficiently large such that \(1<aN<2\). We also prove the multiple existence of solutions for a given decay rate in the case \(aN \ge 2\). Our classification improves previous results which are known only for the case \(0<aN<1\).
Mathematics Subject Classification35J61 35Q75 81T13
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This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01057499).
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