Dark soliton collisions for an N-coupled nonlinear Schrodinger system in the inhomogeneous optical fiber

Under investigation in this paper is an N-coupled variable-coefficient non-linear Schrodinger system, which describes the propagation and collision of the vector optical solitons in the inhomogeneous fiber. Based on the symbolic computation and Hirota method, dark one- and two-soliton solutions for such a system are derived. Propagation and collision of the dark solitons with beta(x) and delta(x), respectively, representing the group velocity dispersion and fiber loss/gain are graphically shown and discussed, where x is the propagation distance. Through the analysis on the dark solitons, we find that the solitons' shapes and collisions depend on beta(x) and delta(x). When beta(x) and delta(x) are chosen as the constants, amplitude and width of a dark one-soliton are unvarying during the propagation, and head-on collision between the dark two solitons is displayed, from which we find that the shapes of the two solitons are the same before and after the collision. When we choose beta(x) as a function of x, propagation directions of the solitons become curved. With beta(x) as a periodic function, dark one-soliton exhibits a periodic oscillation, and oscillating collision between the periodic-type dark two solitons is illustrated with the shapes of the two solitons unchanging. It is found that amplitudes of the dark one- and two-solitons are positively related to delta(x).