On stability of solitons and their attraction for a rotating charge with fixed mass center in the Maxwell field

Abstract

We consider the system of Maxwell equations and Lorentz torque equation which describes a motion of charge in electromagnetic field. Under certain symmetry conditions on charge distribution and on initial fields the mass center of the charge remains fixed and the charge rotates around it. The system admits stationary soliton-type solutions. We study the Lyapunov and the orbital stability of the solitons exploiting the energy conservation law. We also show, by the angular momentum argument, that there is no attraction to a soliton of finite angular momentum on the surface of states of the same angular momentum. The bibliography: 23 refs.