Analytic study on the mixed-type solitons for a (2+1)-dimensional N-coupled nonlinear Schrödinger system in nonlinear optical-fiber communication

Under investigation in this paper is the propagation and interaction of the solitons formed by the incoherently interacting optical beams in the bulk Kerr and saturable media in nonlinear optical fibers, which can be governed by a (2+1)-dimensional N-coupled nonlinear Schrödinger system. Via the symbolic computation and Hirota method, analytic mixed-type vector one- and two-soliton solutions for such a system are derived. The 2-bright-1-dark vector solitons are taken as an example to graphically illustrate the propagation and interaction of the mixed-type vector solitons. Through the analysis on the vector one solitons, the soliton amplitude and width are found to depend on the index of refraction: when the absolute value of the index of refraction increases, the bright soliton amplitude and dark soliton width become larger. Inelastic and elastic overtaking interactions between the bright two solitons, and elastic oblique interaction between the dark two solitons, are illustrated. We see that the bright soliton with a larger amplitude moves faster and overtakes the smaller, and that, increasing the absolute value of the index of refraction, we can obtain the dark soliton with a larger velocity. The soliton amplitudes change during the inelastic interaction, while keep invariant during the elastic interaction.