Fractional optical solitons

This Letter shows that soliton propagation can be described by an extended NLS equation which incorporates fractional dispersion and a fractional nonlinearity. The fractional dispersive term is written in terms of Grünwald–Letnikov fractional derivatives (FDs). Forward and backward FDs are introduced in order to satisfy the conservation of energy. It is found that the soliton solutions of this model form a continuous family and are stable. The Vakhitov–Kolokolov criterion is used to confirm the stability of these fractional solitons.