Collapse arrest in the space-fractional Schrodinger equation with an optical lattice

The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schrodinger equation with Kerr nonlinearity and optical lattice.The approximate analytical soliton solutions are obtained based on the variational approach,which provides reasonable accuracy.Linear-stability analysis shows that all the solitons are linearly stable.No collapses are found when the Levy index 1<α≤2.Forα=1,the collapse is arrested by the lattice potential when the amplitude of perturbations is small enough.It is numerically proved that the energy criterion of collapse suppression in the two-dimensional traditional Schrodinger equation still holds in the one-dimensional fractional Schr odinger equation.The physical mechanism for collapse prohibition is also given.