Accessible solitons of fractional dimension
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Annals of Physics 368 (2016) 110–116
Contents lists available at ScienceDirect
Annals of Physics
journal homepage: www.elsevier.com/locate/aop
Accessible solitons of fractional dimension
Wei-Ping Zhong
a,b,∗
, Milivoj Belić
b
, Yiqi Zhang
c
a
Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province,
Shunde 528300, China
b
Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar
c
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
h i g h l i g h t s
• 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.
a r t i c l e i n f o
Article history:
Received 29 December 2015
Accepted 10 February 2016
Available online 18 February 2016
Keywords:
Fraction-dimensional Schrödinger equation
Strongly nonlocal nonlinear media
Self-similar method
a b s t r a c t
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 so-
lutions of the model are constructed by two special functions,
the associated Legendre polynomials and the Laguerre polynomi-
als 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.
© 2016 Elsevier Inc. All rights reserved.
∗
Corresponding author at: Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province,
Shunde 528300, China.
E-mail address: zhongwp6@126.com (W.-P. Zhong).
http://dx.doi.org/10.1016/j.aop.2016.02.007
0003-4916/© 2016 Elsevier Inc. All rights reserved.
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