Basic fractional nonlinear-wave models and solitons

Boris A. Malomed*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


This review article provides a concise summary of one- and two-dimensional models for the propagation of linear and nonlinear waves in fractional media. The basic models, which originate from Laskin’s fractional quantum mechanics and more experimentally relevant setups emulating fractional diffraction in optics, are based on the Riesz definition of fractional derivatives, which are characterized by the respective Lévy indices. Basic species of one-dimensional solitons, produced by the fractional models which include cubic or quadratic nonlinear terms, are outlined too. In particular, it is demonstrated that the variational approximation is relevant in many cases. A summary of the recently demonstrated experimental realization of the fractional group-velocity dispersion in fiber lasers is also presented.

Original languageEnglish
Article number022102
Issue number2
StatePublished - 1 Feb 2024
Externally publishedYes


FundersFunder number
Israel Science Foundation1695/22


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