Multi-rogue wave solutions for a generalized integrable discrete nonlinear Schrödinger equation with higher-order excitations

In this paper, we construct the discrete higher-order rogue wave (RW) solutions for a generalized integrable nonlinear Schrödinger (NLS) equation. First, based on modified Lax pair, version of Darboux transformation is constructed. Second, dynamical behaviors first-, second- and third-order RW are investigated in corresponding to unique spectral parameter, term coefficient, free constants. The differences between solution NLS equation that Ablowitz–Ladik (AL) illustrated figures. Moreover, explore numerical experiments, which demonstrates strong-interaction RWs stabler than weak-interaction RWs. Finally, modulation instability continuous waves studied.