Fractional optical solitons. (English) Zbl 1236.35167
Summary: 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.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35R11 | Fractional partial differential equations |
| 35C08 | Soliton solutions |
| 81U30 | Dispersion theory, dispersion relations arising in quantum theory |
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