Nonautonomous discrete rogue wave solutions and interactions in an inhomogeneous lattice with varying coefficients

In this paper we analytically investigate nonautonomous discrete rogue wave solutions and their interactions in the generalized Ablowitz–Ladik–Hirota lattice with variable coefficients, which possess complicated wave propagation in time and differ from the usual discrete rogue waves. When the amplitude of the tunnel coupling coefficient between sites decreases, these nonautonomous discrete rogue wave solutions become localized in time after they propagate over some certain large critical values. Moreover, we find that the interactions between nonautonomous discrete rogue wave solutions are elastic.