Bilinear forms and bright-dark solitons for a coupled nonlinear Schrodinger system with variable coefficients in an inhomogeneous optical fiber

Optical fiber communication becomes one of the main pillars of modern communication. In this paper, we study a coupled nonlinear Schrodinger system with variable coefficients, which can describe the simultaneous propagation of the M-field components in an inhomogeneous optical fiber, where M is a positive integer. When M = 2, the bilinear forms are constructed with the Hirota method and the N-bright-dark soliton solutions in terms of the Grammian can be obtained via the Kadomtsev-Petviashvili hierarchy reduction, where N is a positive integer. With the asymptotic analysis and graphic analysis, we find that the amplitudes of one-bright-dark solitons and the background in the dark components exhibit the periodic oscillations. Without the amplification/absorption effect, elastic interaction between the two-bright-dark solitons which keep both the amplitudes and the wave backgrounds invariant is demonstrated. Particularly, we find inelastic interaction between the two-bright-dark solitons, which possess the V-shape profiles in the zero background components and the Y-shape profiles in the periodic oscillating background components. The bound-state soliton under that inelastic condition is also shown. Besides, we present the bound-state bright-dark solitons with varying amplitudes. Furthermore, the analysis of the N-bright-dark soliton solutions are extended to those with M > 2, and as an example, inelastic interaction of the solitons with the case of M = 4 is presented.