LAUSR

In this paper, we have investigated the localization of an input spatial soliton as it propagates through a system where can be described by a fractional Schrodinger equation. In order to solve the Schrodinger equation, we have used a split-step Fourier method. We have also precisely presented the algorithm. We have found that by increasing the Levy index α the wave localization increases while the dispersion of the soliton decreases. Also, by increasing the parameter α, the amplitude of the oscillations decreases and the wave becomes more localized. By using the fractional parameter α, both peak intensity and position of the peak intensity can be tuned along the propagation distance. Finally, by decreasing the fractional parameter α the initial beam undergoes asymmetric diffraction with the position of the peak intensity moving toward positive x-axis and the symmetry of the input beam envelop breaks.