  We introduce 1D and 2D models of a degenerate bosonic gas composed of ions
with positive and negative charges (cations and anions). The system may exist
in the mean-field condensate state, enabling the competition of the Coulomb
coupling, contact repulsion, and kinetic energy of the particles, provided that
their effective mass is reduced by means of a lattice potential. The model
combines the Gross-Pitaevskii (GP) equations for the two-component wave
function of the cations and anions, coupled to the Poisson equation for the
electrostatic potential mediating the Coulomb coupling. The contact interaction
in the GP system can be derived, in the Thomas-Fermi approximation, from a
system of three GP equations, which includes the wave function of heavy neutral
atoms. In the system with fully repulsive contact interactions, we construct
stable spatially periodic patterns (density waves, DWs). The transition to DWs
is identified by analysis of the modulational instability of a uniformly mixed
neutral state. The DW pattern, which represents the system's ground state (GS),
is predicted by a variational approximation. In 2D, a stable pattern is
produced too, with a quasi-1D shape. The 1D system with contact self-attraction
in each component produces bright solitons of three types: neutral ones, with
fully mixed components; dipoles, with the components separated by the
inter-species contact repulsion; and quadrupoles, with a layer of one component
sandwiched between side lobes formed by the other. The transition from the
neutral solitons to dipoles is accurately modeled analytically. A chart of the
GSs of the different types (neutral solitons, dipoles, or quadrupoles) is
produced. Different soliton species do not coexist as stable states. Collisions
between traveling solitons are elastic for dipole-dipole pairs, while
dipole-antidipole ones merge into stable quadrupoles via multiple collisions.
