Nonautonomous discrete rogue waves and interaction in the generalized   Ablowitz-Ladik-Hirota lattice with variable coefficients
  We analytically investigate the nonautonomous discrete rogue wave solutions and their interaction in the generalized Ablowitz-Ladik-Hirota lattice with variable coefficients, which possess complicated wave propagations in time and are beyond 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 interaction between nonautonomous discrete rogue waves is elastic. In particular, these results can reduce to the usual discrete rogue wave solutions when the gain or loss term is ignored. 
Zhenya Yan, Dongmei Jiang, and W. M. Liu
nlin.SI math-ph math.MP