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Accessible solitons of fractional dimension |
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| Authors: | Wei-Ping Zhong Milivoj Beli? Yiqi Zhang |
| Institution: | 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 |
| 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. |
| Keywords: | Fraction-dimensional Schrö dinger equation Strongly nonlocal nonlinear media Self-similar method |
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