We investigate the nonlinear dynamics of (1+1)-dimensional optical beam in the system described by the space-fractional Schrödinger equation with the Kerr nonlinearity. Using the variational method, the analytical soliton solutions are obtained for different values of the fractional Lévy index $\alpha$. All solitons are demonstrated to be stable for $1<\alpha \le 2$. However, when $\alpha =1$, the beam undergoes a catastrophic collapse (blow-up) like its counterpart in the (1+2)-dimensional system at $\alpha =2$. The collapse distance is analytically obtained and a physical explanation for the collapse is given.

• Received 4 June 2018

DOI:https://doi.org/10.1103/PhysRevE.98.022211