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

The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schrödinger 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 Lévy index 1<α≤2. For α=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 Schrödinger equation still holds in the one-dimensional fractional Schrödinger equation. The physical mechanism for collapse prohibition is also given.