Exhaustive derivation of static self-consistent multi-soliton solutions in the matrix Bogoliubov-de Gennes systems

Abstract

The matrix-generalized Bogoliubov-de Gennes systems have recently been considered by the present author [arXiv:1509.04242, Phys. Rev. B 93, 024512 (2016)], and time-dependent and self-consistent multi-soliton solutions have been constructed based on the ansatz method. In this paper, restricting the problem to the static case, we exhaustively determine the self-consistent solutions using the inverse scattering theory. Solving the gap equation, we rigorously prove that the self-consistent potential must be reflectionless. As a supplementary topic, we elucidate the relation between the stationary self-consistent potentials and the soliton solutions in the matrix nonlinear Schrödinger equation. Asymptotic formulae of multi-soliton solutions for sufficiently isolated solitons are also presented.

32 pages, 3 figures, final version published in PTEP

References in corpus (8)

• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Degenerate Fermi Gases of Ytterbium
• Dark solitons in F=1 spinor Bose--Einstein condensate
• Inverse scattering method for square matrix nonlinear Schrödinger equation under nonvanishing boundary conditions
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy
• Spin imbalance effect on Larkin-Ovchinnikov-Fulde-Ferrel state
• Exact solution of N baryon problem in the Gross-Neveu model

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