Optical discrete rogue wave solutions and numerical simulation for a coupled Ablowitz–Ladik equation with variable coefficients

Abstract

We study the dynamics of discrete rogue waves in an array of nonlinear waveguides. Some non-autonomous discrete rogue wave solutions and their interactions in the coupled Ablowitz–Ladik (CAL) equation with variable coefficients are considered. And these problems possess complicated wave propagations in time and differ from the single discrete rogue waves. Furthermore, we predict the long-living rogue wave solutions of the discrete CAL equation. In addition, the controllable behaviors of this non-autonomous rogue wave system with the nonlinearity management parameters are discussed. At last, the numerical simulations on the evolution and collision of two rogue waves are performed to verify the prediction of the analytical formulations. These results may be useful to explain some nonlinear wave phenomena in certain electrical and optical systems.