Dynamics of periodic wave evolution and collision for a two-component Ablowitz–Ladik system on the two physically uncoupled chains with the next-to-neighboring dispersion

Using the Ablowitz–Kaup–Newell–Segur production method, a second-order Ablowitz–Ladik lattice system with the 4× 4 Lax pair is presented and is being investigated in this article. This system could serve as a theoretical reference for the propagation of wave signals in optical and electrical transmission lines employing artificial synchronization technology. Firstly, based on the 4× 4 Lax pair, the discrete N -fold Darboux transformation is constructed, and myriad conservation laws are derived. Then, the analytic solutions are investigated and discussed graphically via the resulting Darboux transformation, which exhibit abundant wave structures such as classical bright solitons, novel periodic waves, multi-peak solitons, classical and novel breathers, and some of their elastic collision structures that are different from the results for previously known systems of Ablowitz–Ladik type. These unexpected findings are caused by the artificial synchronization of physically independent signals propagating along two separate physically uncoupled chains. Besides, the asymptotic analysis method is used to accurately derive several important physical quantities for two-soliton solutions. Finally, the dynamics concerning several representative one-soliton and one-breather structures are analyzed via numerical simulations. What we obtained in this paper may be helpful for interpreting some more complex wave signal propagation phenomena that occur when the synchronization technique is applied to specific optical and electrical systems consisting of several physically uncoupled subsystems.