We exhaust all exact self-consistent solutions of complex-valued fermionic condensates in the ($1+1$)-dimensional Bogoliubov–de Gennes and chiral Gross-Neveu systems under uniform boundary conditions. We obtain $n$ complex (twisted) kinks, or gray solitons, with $2n$ parameters corresponding to their positions and phase shifts. Each soliton can be placed at an arbitrary position while the self-consistency requires its phase shift to be quantized by $\pi /N$ for $N$ flavors.

• Received 27 September 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.131601