Basic fractional nonlinear-wave models and solitons release_hlhct6qfrrbolijvn6uqkn3r6e

by Boris Malomed

Published in Chaos by AIP Publishing.

2024   Volume 34, Issue 2

Abstract

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.
In application/xml+jats format

Archived Files and Locations

application/pdf   2.6 MB
file_rbxilclsafe6fgfjwotxz4djzq
watermark.silverchair.com (publisher)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article-journal
Stage   published
Date   2024-02-01
Language   en ?
DOI  10.1063/5.0190039
PubMed  38341765
Container Metadata
Not in DOAJ
In Keepers Registry
ISSN-L:  1054-1500
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: e770070e-7d18-4b7e-87f6-55a69538a85a
API URL: JSON