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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. [ABSTRACT FROM AUTHOR]