Novel computational and accurate numerical solutions of the modified Benjamin–Bona–Mahony (BBM) equation arising in the optical illusions field

This research is based on three main pillars which are studying the computational solutions of the modified Benjamin–Bona–Mahony (BBM) equation via the modified Khater method then investigating the stability property of the obtained solutions through the Hamiltonian system’s features, evaluating the initial and boundary conditions that allow applying the B-spline collection schemes (cubic, quantic, septic) to find the numerical solutions of the suggested model and to explain the matching between our obtained types of solutions. This model is used in the optical illusions field by describing the propagation of long waves in the nonlinear dispersive media in a visual illusion. An optical illusion is an illusion caused by the visual system and characterized. Four distinct types of sketches (2D, 3D, contour, and Stream plots) have been employed for better understanding our obtained solutions and their convergence.