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Abstract
The time-dependent field equations of the nonlinear field systems, whose static soliton solutions are (global) vortex strings, are studied by a numerical approach. They concern (i) the theory of a single complex scalar field with a spontaneously broken U(1) symmetry, and (ii) the system of a complex scalar field doublet with an approximate U(2) symmetry. The obtained numerical solutions allow to clarify the dynamical behaviors of the systems under fluctuations. The systems are shown to have order-chaos phase transitions, but, despite phase transitions and deformations in field profiles by fluctuations, the shapes of the total field energy density distributions are rather stable.
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