Abstract
An analytical and numerical investigation of the propagation of optical beams in Kerr term-like saturable photorefractive media is performed. The major problem studied is the instability of beam propagation in nonlinear self-focusing optical media. The numerical technique employed is the Runge-Kutta finite-difference method. The resulting soliton-like structures propagate and develop modulational instabilities which lead to the breakup of simple beam arrangements into more complex ones. The direct numerical simulation of the nonlinear Schrodinger's equation with saturable law nonlinearity is performed and the results are compared to soliton-like structures resulting from square-root law nonlinearity. Gaussian, super-Gaussian, sech and super-sech pulses are obtained. In addition, the ordinary differential equation that is obtained by the traveling wave ansatz is also studied numerically, with appropriate initial condition, leading to a non-traveling wave-like solution