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Title: Accessible solitons of fractional dimension

Abstract

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.

Authors:
 [1];  [2];  [3]
  1. Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China)
  2. Texas A&M University at Qatar, P.O. Box 23874, Doha (Qatar)
  3. Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
Publication Date:
OSTI Identifier:
22560317
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 368; Journal Issue: Complete; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; ASYMMETRY; LAGUERRE POLYNOMIALS; LAPLACIAN; LAYERS; LEGENDRE POLYNOMIALS; NONLINEAR PROBLEMS; POTENTIALS; SCHROEDINGER EQUATION; SOLITONS

Citation Formats

Zhong, Wei-Ping, Texas A&M University at Qatar, P.O. Box 23874, Doha, Belić, Milivoj, and Zhang, Yiqi. Accessible solitons of fractional dimension. United States: N. p., 2016. Web. doi:10.1016/J.AOP.2016.02.007.
Zhong, Wei-Ping, Texas A&M University at Qatar, P.O. Box 23874, Doha, Belić, Milivoj, & Zhang, Yiqi. Accessible solitons of fractional dimension. United States. https://doi.org/10.1016/J.AOP.2016.02.007
Zhong, Wei-Ping, Texas A&M University at Qatar, P.O. Box 23874, Doha, Belić, Milivoj, and Zhang, Yiqi. 2016. "Accessible solitons of fractional dimension". United States. https://doi.org/10.1016/J.AOP.2016.02.007.
@article{osti_22560317,
title = {Accessible solitons of fractional dimension},
author = {Zhong, Wei-Ping and Texas A&M University at Qatar, P.O. Box 23874, Doha and Belić, Milivoj and Zhang, Yiqi},
abstractNote = {We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.},
doi = {10.1016/J.AOP.2016.02.007},
url = {https://www.osti.gov/biblio/22560317}, journal = {Annals of Physics},
issn = {0003-4916},
number = Complete,
volume = 368,
place = {United States},
year = {Sun May 15 00:00:00 EDT 2016},
month = {Sun May 15 00:00:00 EDT 2016}
}