Truncated-Bloch-wave solitons in nonlinear fractional periodic systems

We address the existence and stability properties of localized truncated-Bloch-wave solitons in one-dimensional nonlinear fractional Schrodinger equation with an optical lattice. Under a defocusing nonlinearity, extended nonlinear Bloch waves with finite amplitudes bifurcate from linear Bloch modes at band edges. The variation of Levy index has a profound impact on the existence, profile, power and stability of nonlinear modes. Truncated-Bloch-wave solitons with different number of units are found in finite bandgaps. The main body of truncated-Bloch-wave soliton coincides exactly with the corresponding nonlinear Bloch wave. While solitons residing in the second gap propagate stably in a narrow region, nonlinear states in the first gap are stable in almost their whole existence domains. Specially, the instability of solitons can be significantly suppressed by the decrease of Levy index. (C) 2019 Elsevier Inc. All rights reserved.