Under consideration are the coupled Ablowitz–Ladik lattice equations with branched dispersion, which may be used to model the propagation of an optical field in a tight binding waveguide array. The discrete generalized $(m,N-m)$-fold Darboux transformation based on 2 × 2 Lax pair is extended to construct rogue wave solutions for this discrete coupled system with 4 × 4 Lax pair. Novel position controllable rogue wave with multi peaks and depressions and mixed interaction structures of breather and rouge wave are shown graphically. It is clearly shown that these new discrete rogue wave structures in this coupled system are different from those of the single component Ablowitz–Ladik equation. These results may be useful to explain some physical phenomena in nonlinear optics.

正在考虑的是具有分支色散的耦合 Ablowitz-Ladik 晶格方程，该方程可用于模拟紧束缚波导阵列中光场的传播。离散广义$(米,N-米)$基于 2 × 2 Lax 对的 -fold Darboux 变换被扩展以构建具有 4 × 4 Lax 对的离散耦合系统的流氓波解。图形显示了具有多峰和凹陷以及呼吸和胭脂波的混合相互作用结构的新型位置可控流氓波。清楚地表明，该耦合系统中的这些新的离散流氓波结构与单分量 Ablowitz-Ladik 方程的结构不同。这些结果可能有助于解释非线性光学中的一些物理现象。