On the existence of Q–Monopole–Ball soliton with unit magnetic charge

We establish the existence of a spherically symmetric solution with unit magnetic charge in a recently formulated Q–Monopole–Ball (QMB) model. The solution carries both topological and non-topological charges and generalizes the classical 't Hooft–Polyakov monopole. We show that the system degenerates into a pure monopole state under a critical parameter condition. The existence of the QMB solution indicates a new non-gravitational mechanism for binding like-charged monopoles and offers a constructive framework for exploring more complex field configurations. By employing a two-step iterative shooting approach and the maximum principle, we construct a solution with monotone components and characterize the asymptotic behaviors. Our study confirms previous numerical simulations and provides theoretical support for the realization of QMBs in the early universe. • The existence of Q-Monopole-Ball soliton with unit magnetic charge is established. • The shooting method combined with fixed-point theory derives a monotone solution. • The solution generalizes the classical 't Hooft-Polyakov monopole. • Qualitative properties are consistent with previous numerical simulations.