2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142586Abelian gauge theories consist of a class of field equations which provide a model for the interaction between matter and electromagnetic fields. In this paper we analyze the existence of solitary waves for these theories. We assume that the lower order term W is positive and we prove the existence of solitary waves if the coupling between matter and electromagnetic field is small. We point out that the positiveness assumption on W implies that the energy is positive: this fact makes these theories more suitable to model physical phenomena.27 pagesAnalysis of PDEsMathematical Physics35J50; 81T13text