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

SU(N) affine Toda solitons and breathers from transparent Dirac potentials