  The (1+1)-dimensional gauge model of two complex self-interacting scalar
fields that interact with each other through an Abelian gauge field and a
quartic scalar interaction is considered. It is shown that the model has
nontopological soliton solutions describing soliton systems consisting of two
Q-ball components possessing opposite electric charges. The two Q-ball
components interact with each other through the Abelian gauge field and the
quartic scalar interaction. The interplay between the attractive
electromagnetic interaction and the repulsive quartic interaction leads to the
existence of symmetric and nonsymmetric soliton systems. Properties of these
systems are investigated by analytical and numerical methods. The symmetric
soliton system exists in the whole allowable interval of the phase frequency,
whereas the nonsymmetric soliton system exists only in some interior
subinterval. Despite the fact that these soliton systems are electrically
neutral, they nevertheless possess nonzero electric fields in their interiors.
It is found that the nonsymmetric soliton system is more preferable from the
viewpoint of energy than the symmetric one. Both symmetric and nonsymmetric
soliton systems are stable to the decay into massive scalar bosons.
