Dark solitons for a discrete variable-coefficient Ablowitz-Ladik equation for an electrical/optical system

摘要

Under investigation in this paper is a discrete variable-coefficient Ablowitz-Ladik equation, which has certain applications in the electrical and optical systems. Employing the Hirota method and symbolic computation, we obtain the dark one- and two-soliton solutions under a variable-coefficient constraint. Linear-, parabolic-, periodic- and s-shaped dark one solitons are observed: We find that the space-time-modulated inhomogeneous frequency shift only affects the velocity of the dark soliton, the coefficient of tunnel coupling between the sites only affects the amplitude of the dark soliton, the time-modulated effective gain/loss term has no effect on either the dark soliton's velocity or amplitude, and the velocity of the dark soliton decreases as the lattice spacing increases with the amplitude unchanged. Via the asymptotic analysis, we prove that the interactions between the dark two solitons are elastic on the soliton solutions. Overtaking interactions between the linear- and parabolic-shaped dark two solitons, as well as parallel linear- and s-shaped dark two solitons are plotted.