Solitons in three space dimensions as a model for relativistic particles

This paper gives a short report of research carried out in the last five years on the existence of solitons in three space dimensions. Benci, Fortunato and Pisani have developed a model equation proposed in 1964 by C.H. Derrick. Using some recent techniques of nonlinear functional analysis, the existence of a non-trivial solitary wave, with a topological constraint, has been proved. Subsequent research has demonstrated the relativistic behaviour of these waves, multiplicity results and the interaction with the electromagnetic held.