Solitons in gauge theories: existence and dependence on the charge

Abstract

In this paper we review recent results on the existence of non-topological solitons in classical relativistic nonlinear field theories. We follow the Coleman approach, which is based on the existence of two conservation laws, energy and charge. In particular we show that under mild assumptions on the nonlinear term it is possible to prove the existence of solitons for a set of admissible charges. This set has been studied for the nonlinear Klein-Gordon equation, and in this paper we state new results in this direction for the Klein-Gordon-Maxwell system.