Compact Q-balls and Q-shells in a scalar electrodynamics

We investigate spherically symmetric nontopological solitons in electrodynamics with a scalar field self-interaction U similar to|psi| taken from the complex signum-Gordon model. We find Q-balls for small absolute values of the total electric charge Q, and Q-shells when |Q| is large enough. In both cases the charge density exactly vanishes outside certain compact regions in the three-dimensional space. The dependence of the total energy E of small Q-balls on the total electric charge has the form E similar to|Q|(5/6), while in the case of very large Q-shells, E similar to|Q|(7/6).