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In this Letter, we study a nonlocal vector nonlinear Schrödinger (NVNLS) equation with self-induced parity-time-symmetric potential. We construct the N -fold Darboux transformation in terms of compact determinant forms. Starting from the non-vanishing background, we give the general solution of spectral problem, which allows us to derive many different types of exact analytical solutions of the NVNLS equation, like the breathers, dark and anti-dark solitons. With three-component case as an example, we display three types of two-soliton elastic collision behaviors: breather and dark soliton, breather and anti-dark soliton, dark soliton and anti-dark soliton. [ABSTRACT FROM AUTHOR]

In this Letter, the Darboux transformation is first applied to the defocusing Sasa–Satsuma equation which describes the propagation dynamics of ultrashort light pulses in the normal dispersion regime of optical fibers. The N -fold iterative transformation is expressed in terms of the determinants. This transformation enables us to construct explicit analytical dark soliton solutions from non-vanishing background. In illustration, the single-dark soliton solution is presented from the once-iterated formula. [ABSTRACT FROM AUTHOR]