Mathematical modeling of diffraction instability in optical bistable system Original Research Article

We investigate the space and time instability of a self-focusing light beam by means of mathematical modeling in the cavity-free optical bistability (OB) system. The mathematical model of the considered process consists of the nonlinear Schrödinger equation having the Laplace operator in polar coordinates and the nonlinear diffusion equation. A nonlinear conservative monotone difference scheme is constructed for this problem. To adapt the elaborated numerical algorithm to multiprocessor computer systems we apply the Domain Decomposition Method (DDM). We study the development of the axial self-focusing beam instability due to the azimuth perturbation of the initial profile of a beam.