On the existence of stable charged Q-balls

This paper concerns hylomorphic solitons, namely, stable, solitary waves whose existence is related to the ratio energy/charge. In theoretical physics, the name Q-ball refers to a type of hylomorphic solitons or solitary waves relative to the nonlinear Klein-Gordon equation. We are interested in the existence of charged Q-balls, namely, Q-balls for the nonlinear Klein-Gordon equation coupled with the Maxwell equations. In this case, the charge reduces to the electric charge. The main result of this paper establishes that stable, charged Q-balls exist provided that the interaction between the matter and the gauge field is sufficiently small.