A numerical study of optical soliton-like structures resulting from the nonlinear Schrödinger's equation with square-root law nonlinearity

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 by the Runge-Kutta finite-difference numerical technique. 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 Schrödinger's equation with square-root law nonlinearity is performed. Gaussian, super-Gaussian, and sech pulses are obtained numerically. Finally the ordinary differential equation that is obtained by the traveling wave ansatz is also studied numerically, with appropriate initial condition, leading to a traveling wave-like solution.