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

在本文中，我们构造了广义可积离散非线性薛定谔 (NLS) 方程的离散高阶流氓波 (RW) 解。首先，基于修正的 Lax 对，构造了广义 Darboux 变换的离散版本。其次，研究了与唯一谱参数、高阶项系数和自由常数相对应的一阶、二阶和三阶 RW 解的动力学行为。高阶离散 NLS 方程的 RW 解与 Ablowitz-Ladik (AL) 方程的 RW 解之间的差异如图所示。此外，我们探索了数值实验，这表明强交互 RW 比弱交互 RW 更稳定。最后，研究了连续波的调制不稳定性。