Soliton Solutions of an Integrable Coupled Discrete Nonlocal Nonlinear Schrdinger Equation

This study employs Hirotas bilinear method to derive exact solutions for the coupled discrete non-local nonlinear Schrdinger (NLS) equation. The equation under investigation is derived from the non-local reduction of the coupled discrete nonlinear NLS equation, which arises in various physical contexts such as nonlinear optics and Bose-Einstein condensates. Exact solutions of coupled discrete non-local NLS equations are obtained, including bright-bright one-soliton solutions, two-soliton solutions, and dark-dark soliton solutions. For the dark-dark soliton solution, the construction of the solution and the bilinear expansion are derived from the continuous system, but the continuous system solved in this way yields a breathing solution, however, in this coupled discrete non-local NLS equation, under specific parameters, we obtain coupled dark-dark soliton waves. In addition, periodic solutions, singular solutions and double spatial period solutions are obtained by taking different parameters. The soliton dynamics are visualized using mathematical software, providing insights into their behavior and interactions. This work enhances the understanding of soliton solutions in discrete non-local systems and provides a practical approach for analyzing similar nonlinear wave phenomena.