Periodic and localized wave patterns for coupled Ablowitz-Ladik systems with negative cross phase modulation

A new system of coupled Ablowitz-Ladik equations is introduced where cubic nonlinearities from intensities of both waveguide arrays are included. The Hirota bilinear transform is formulated and is used to derive breathers periodic in space or time. One spatially periodic solution is utilized to verify the lowest order conservation laws. Algebraically localized rogue wave modes with pulsating properties are obtained from breathers in the limit of large wave periods. Incorporating additional modes of cubic nonlinearities, namely, cross phase modulations, in two arrays of oscillators on an integer lattice can further enhance the modeling capability in optical physics.