Abelian gauge theories consist of a class of ?eld equations which pro- vide a model for the interaction between matter and electromagnetic ?elds. In this paper we analyze the existence of solitary waves for these theo- ries. We assume that the lower order term W is positive and we prove the existence of solitary waves if the coupling between matter and elec- tromagnetic ?eld 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.
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