Multi-dark soliton solutions for the higher-order nonlinear Schrödinger equation in optical fibers

In optical fibers with the higher-order dispersive and nonlinear effects, the propagation of the ultrashort pulse can be governed by the higher-order dispersive nonlinear Schrödinger equation. In this paper, the binary Darboux transformation is applied to this higher-order model, and the n-times iterative transformation is expressed in terms of the determinants. By the limit technique, the multi-dark soliton solutions are derived from the nonzero background. Based on obtained solution, the elastic collisions between two and among three-dark solitons with different velocities are presented. The bound-state dark solitons can be also formed when two-dark solitons with the same velocity propagate in parallel.