Classical vortex solution of the Abelian Higgs model

An exact vortex solution for the Abelian Higgs model is found when a particular relation between the coupling constants is satisfied. For this case (in which the masses of the scalar and vector bosons are the same), we decouple the classical field equations and solve them. We obtain power-series expansions and asymptotic expressions for the solution. The values of the fields are explicitly calculated for a one-quantum-of-flux solution, and bounds are established for the $n$-quanta case. Finally, we discuss the field form factors.