In this letter, we propose a new semi-discrete complex coupled system associated with 4 × 4 Lax pair. Firstly, the continuous limit technique is used to map this semi-discrete system to two new continuous complex equations. Then, the discrete generalized $(m,N-m)$-fold Darboux transformation for this system is first proposed. Finally, through applying the resulting Darboux transformation, some novel rogue wave and periodic wave structures with position adjustable parameters are investigated and discussed graphically. In particular, it is found that in the same semi-discrete system, the first-order rogue wave can have one or two fundamental rogue waves, and the second-order rogue wave can have three or six fundamental rogue waves.

在这封信中，我们提出了一个新的与 4 × 4 Lax 对相关的半离散复耦合系统。首先，使用连续极限技术将这个半离散系统映射到两个新的连续复方程。然后，离散广义$(米,ñ-米)$首次提出了该系统的-fold Darboux 变换。最后，通过应用所得到的Darboux变换，对一些具有位置可调参数的新颖的流氓波和周期波结构进行了研究和图形化讨论。特别是发现在同一个半离散系统中，一阶流氓波可以有一个或两个基波流氓波，二阶流氓波可以有三个或六个基波流氓波。