Soliton Interactions and Collision Dynamics in a Variable-Coefficient Coupled Nonlocal Nonlinear Schrödinger Systems

The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method. The two-soliton and double-hump one-soliton solutions for the equations are first obtained. By assigning different functions to the variable coefficients, we obtain V-shaped, Y-shaped, wave-type, exponential solitons, and so on. Next, we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions. Finally, by setting different wave numbers, we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions. This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.