In this study, an efficient fourth-order conservative explicit numerical scheme using method of lines is developed to simulate different scenarios of soliton interactions and reflections for a (2 + 1)-dimensional coupled nonlinear Schrödinger (CNLS) system. The fourth-order Runge–Kutta technique is applied as a time integrator to the resulting ordinary differential system. Both integrable and nonintegrable cases of the CNLS system are considered. A condition for the scheme to be stable is deduced with the aid of von Neumann stability analysis. Several numerical experiments have been carried out to exhibit the reliability of the scheme in capturing and understanding the interesting phenomenon of elastic and inelastic soliton collisions/reflections related to many nonlinear evolution equations. The ability of the scheme to preserve the conserved invariants in long terms confirms its accuracy and stability. New results associated with interactions and reflections of soliton waves are obtained.