Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems

Abstract

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 grey 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.

5 pages for the main article + 7 pages for the supplemental material for a detailed derivation of the solution by the inverse scattering method, 3 figures, final version published in Phys. Rev. Lett

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