Beyond-band discrete soliton interaction in binary waveguide arrays

We investigate different scenarios of interaction between two beyond-band discrete solitons (BBDSs), which are a new class of solitons in binary waveguide arrays and have been investigated just recently. In the quasi-continuous regime when solitons intensity is low and, thus, solitons are broad, two BBDSs with the same envelope in binary waveguide arrays interact with each other practically like two well-known fundamental solitons governed by the nonlinear Schrödinger equation in a single optical fiber. However, this similarity disappears if the discrete nature of the system is enhanced by increasing the intensity of BBDSs. In that case, two initially in-phase BBDSs with the same detuning cannot periodically collide during propagation. We also show that single-peaked BBDSs are more robust and less mobile than double-peaked BBDSs with the same detuning. This robustness stops two identical single-peaked BBDSs from interaction even at initial separations when double-peaked BBDSs can still strongly interact with each other or with single-peaked BBDSs.