Abstract
In this paper, we construct the discrete rogue wave(RW) solutions for a higher-order or generalized integrable discrete nonlinear Schr¨odinger(NLS) equation. First, based on the modified Lax pair, the discrete version of generalized Darboux transformation are constructed. Second, the dynamical behaviors of first-, second- and third-order RWsolutions are investigated in corresponding to the unique spectral parameter λ, higher-order term coefficient γ, and free constants dk, fk (k = 1, 2, · · · ,N), which exhibit affluent wave structures. The differences between the RW solution of the higher-order discrete NLS equation and that of the Ablowitz-Ladik(AL) equation are illustrated in figures. Moreover, numerical experiments are explored, which demonstrates that strong-interaction RWs are stabler than the weak-interaction RWs. Finally, the modulation instability of continuous waves is studied.
Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects