Topological solitary waves with arbitrary charge and the electromagnetic field

Abstract

This paper deals with a model of solitary waves, in three space dimensions, which are characterized by a topological invariant called charge; these waves behave as relativistic particles. We study the interaction with an electromagnetic field. The Lagrangian density of the system is the sum of three terms: the first is that of the free soliton, the second is the classical Lagrangian density of an electromagnetic field, the third, which is due to the interaction, is chosen so that the electric charge coincides with the topological charge. We prove the existence of a static solution for every fixed value of the charge. The energy functional is strongly unbounded from above, as from below; after a reduction argument, the critical points are found by means of the Principle of Symmetric Criticality.