A Lagrangian for Electromagnetic Solitary Waves in Vacuum

A system of equations, describing the evolution of electromagnetic fields, is introduced and discussed. The model is strictly related to Maxwell's equations. As a matter of fact, the Lagrangian is the same, but the variations are subjected to a suitable constraint. This allows to enlarge the space of solutions, including for example solitary waves with compact support. In this way, without altering the physics, one is able to deal with vector waves as they were massless particles. The main properties of the model, together with numerous exact explicit solutions are presented.