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Recently the most general static self-consistent multi-soliton solutions inBogoliubov-de Gennes and chiral Gross-Neveu systems are derived by the presentauthors [D. A. Takahashi and M. Nitta, Phys. Rev. Lett. 110, 131601 (2013)].Here we show a few complementary results, which were absent in the previous ourwork. We prove directly from the gap equation that the self-consistentsolutions need to have reflectionless potentials. We also give theself-consistent condition for the system consisting of only right-movers, whichis more used in high-energy physics.

On reflectionless nature of self-consistent multi-soliton solutions in Bogoliubov-de Gennes and chiral Gross-Neveu models