Discrete bright–dark soliton solutions and parameters controlling for the coupled Ablowitz–Ladik equation

Abstract

We consider the nonautonomous discrete vector bright–dark solutions and their controllable behaviors in the coupled Ablowitz–Ladik equation with variable coefficients, which possesses complicated wave propagation in time. Based on the differential–difference symmetry transformation and the Lame polynomial solutions, we use the Jacobi elliptic functions $$\hbox {sn}(n, m), \hbox {cn}(n, m)$$ , $$\hbox {dn}(n, m)$$ and present the nonautonomous discrete vector bright–dark solutions, which are localized in space and keep the localization longer in time. Moreover, we also exhibit the wave propagation of nonautonomous Lame polynomial solutions of higher order and their dynamics for some chosen parameters and functions. And the managements and dynamic behaviors of these solutions are investigated analytically.