  Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac
equation play an important role as self-consistent mean fields in 1+1
dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and
quasi-one dimensional superconductors (Bogoliubov-De Gennes equation). Here, we
show that they also serve as seed to generate a large class of classical
multi-soliton and multi-breather solutions of su(N) affine Toda field theories,
including the Lax representation and the corresponding vector. This generalizes
previous findings about the relationship between real kinks in the Gross-Neveu
model and classical solitons of the sinh-Gordon equation to complex twisted
kinks.
