Darboux transformation and soliton solutions of the nonlocal Heisenberg spin system with self-consistent potential

In this paper, we investigate non-locality properties of the generalized Heisenberg spin system in the presence of self-consistent potential (called the M-XCIX system) according to the nonlocal gauge equivalence between it and the nonlocal nonlinear Schrödinger and the Maxwell–Bloch (NLS-MB) system. Then we construct a Darboux transformation for the nonlocal M-XCIX system and further generalize it to the matrix form of the [Formula: see text]-fold Darboux transformation of this system. Finally, in terms of a proper trivial seed solution, we derive one-soliton solutions and the computation formula of nonlocal two-soliton solutions and multi-soliton solution.