Some discrete soliton solutions and interactions for the coupled Ablowitz–Ladik equations with branched dispersion

Abstract

The coupled Ablowitz-Ladik lattice equations are the integrable discretizations of the Schrödinger equation, which can be used to model the propagation of an optical field in a tight binding waveguide array. In this paper, the discrete N-fold Darboux transformation(DT) is used to derive the discrete breather and bright soliton solutions of coupled Ablowitz–Ladik equations. Soliton interaction structures of obtained solutions are shown graphically. Based on 4 × 4 discrete Lax pairs, the transformation matrix T of DT is constructed. Then, we derive novel discrete one-soliton and two-soliton with the zero and nonzero seed solutions. And the dynamic features of breather and bright solutions are displayed, some soliton interaction phenomena are shown in the coupled Ablowitz-Ladik lattice equations. These results may be useful to explain some nonlinear wave phenomena in certain electrical and optical systems.