We present explicit solutions of the signum-Gordon scalar field equation
which have finite energy and are periodic in time. Such oscillons have a
strictly finite size. They do not emit radiation.Comment: 12 pages, 4 figure
We investigate spherically symmetric non topological solitons in electrodynamics with a scalar field self interaction U ∼ |ψ| 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 .
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