In this paper we study the Nonlinear Schr\"odinger-Maxwell equations (NSM).
We are interested to analyse the existence of solitons, namely of finite energy
solutions which exhibit stability properties. This paper is divided in two
parts. In the first, we give an abstract definition of soliton and we develope
an abstract existence theory. In the second, we apply this theory to NSM.Comment: arXiv admin note: substantial text overlap with arXiv:1212.323