Competition of parabolic and periodic sinusoidal potential in the propagation of a soliton

In this paper, we investigate the soliton propagation through Kerr media and saturable Kerr media. In order to solve the nonlinear Schrödinger equation we use split-step Fourier method. We show that in the Kerr media, by changing the maximum potential depth or the spatial frequency, the oscillation period of solitons changes. It is seen that there are two critical spatial frequenciessc1 = 1.9 and sc2 = 2.6. The oscillation period decreases by increasing the spatial frequency from 1 to sc1and increases by increasing s from sc1to sc2 and finally does not vary for s > sc2. In the saturable Kerr media, the maximum intensity decreases by increasing the saturable nonlinearity.