  Exciton effects on conjugated polymers and the resulting optical
nonlinearities are investigated in soliton lattice systems. The magnitude of
the THG at the 10 percent doping increases by the factor about 10^2 from that
of the neutral system. The huge increase by the order two is common for several
choices of Coulomb interaction strengths, and is seen in open systems as well
as in periodic systems. We also find that the THG enhances much larger when the
number of solitons is two in the open boundaries. This new fact should be
attractive to the experimentalists.
  Keywords: Semi-empirical models and model calculations, Electron density and
excitation spectra calculations, Many-body and quasiparticle theories,
Low-bandgap conjugated polymers
