  We study the self-interaction effects for the Dirac particle moving in an
external field created by static charges in (1+1)-dimensions. Assuming that the
total electric charge of the system vanishes, we show that the asymptotically
linearly rising part of the external potential responsible for nonexistence of
bound states in the external field problem without self-interaction is
cancelled by the self-potential of the zero mode of the Dirac particle charge
density. We derive the Dirac equation which includes the self-potential of the
non-zero modes and is nonlinear. We solve the spectrum problem in the case of
two external positive charges of the same value and prove that the Dirac
particle and external charges are confined in a stable system.
