Propagation of Airy-Gaussian beam in Kerr medium

By using the method of moments, the critical power of the Airy-Gaussian (AiG) beam is given for different decay factors and different distribution factors numerically. The critical power P-cr of the AiG beam decreases as the distribution factor increases. Using the split-step Fourier method, the propagations of the AiG beam in the free space and in the Kerr medium are shown. It has been found that the self-acceleration effect becomes weaker when the distribution factor increases. As the initial input power increases, we can observe the quasi-breather finally. From the root mean square (rms) beam width and the peak intensity figures, one can see that the beam with large distribution factor is more sensitive to the change of the initial input power.