Compact Q-balls and Q-shells in a scalar electrodynamics
  We investigate spherically symmetric non topological solitons in electrodynamics with a scalar field self interaction U ~|\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 region 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 ~ |Q|^(5/6), while in the case of very large Q-shells E ~ |Q|^(7/6). 
H. Arod\'z and J. Lis