  The first analytic topologically non-trivial solutions in the
(3+1)-dimensional gauged non-linear sigma model representing multi-solitons at
finite volume with manifest ordered structures generating their own
electromagnetic field are presented. The complete set of seven coupled
non-linear field equations of the gauged non-linear sigma model together with
the corresponding Maxwell equations are reduced in a self-consistent way to
just one linear Schrodinger-like equation in two dimensions. The corresponding
two dimensional periodic potential can be computed explicitly in terms of the
solitons profile. The present construction keeps alive the topological charge
of the gauged solitons. Both the energy density and the topological charge
density are periodic and the positions of their peaks show a crystalline order.
These solitons describe configurations in which (most of) the topological
charge and total energy are concentrated within three-dimensional tube-shaped
regions. The electric and magnetic fields vanish in the center of the tubes and
take their maximum values on their surface while the electromagnetic current is
contained within these tube-shaped regions. Electromagnetic perturbations of
these families of gauged solitons are shortly discussed.
