Solitons and dromion-like structures in an inhomogeneous optical fiber

In this paper, a generalized higher-order variable-coefficient nonlinear Schrödinger equation is studied, which describes the propagation of subpicosecond or femtosecond pulses in an inhomogeneous optical fiber. We derive a set of the integrable constraints on the variable coefficients. Under those constraints, via the symbolic computation and modified Hirota method, bilinear equations, one-, two-,three-soliton solutions and dromion-like structures are obtained. Properties and interactions for the solitons are studied: (a) effects on the solitons resulting from the wave number k, third-order dispersion δ₁(z) , group velocity dispersion α(z) , gain/loss Γ₂(z) and group-velocity-related γ(z) are discussed analytically and graphically where z is the normalized propagation distance along the fiber; (b) bound state with different values of α(z) , δ₁(z) , γ(z) and Γ₂(z) are presented where some periodic or quasiperiodic formulae are derived. Interactions between the two solitons and between the bound states and a single soliton are, respectively, discussed; and (c) single, double and triple dromion-like structures with different values of α(z) , δ₁(z) , γ(z) are also presented, distortions of which are found to be determined by those variable coefficients.