Accessible solitons in three-dimensional parabolic cylindrical coordinates |
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Affiliation: | 1. Department of Electronic Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300, China;2. School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China;3. Science Program, Texas A & M University at Qatar, 23874 Doha, Qatar;4. Department of Medical Science, Shunde Polytechnic, Guangdong Province, Shunde 528300, China |
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Abstract: | A class of self-similar beams, named three-dimensional (3D) spatiotemporal parabolic accessible solitons, are introduced in the 3D highly nonlocal nonlinear media. We obtain exact solutions of the 3D spatiotemporal linear Schrödinger equation in parabolic cylindrical coordinates by using the method of separation of variables. The 3D localized structures are constructed with the help of the confluent hypergeometric Tricomi functions and the Hermite polynomials. Based on such an exact solution, we graphically display three different types of 3D beams: the Gaussian solitons, the ring necklace solitons, and the parabolic solitons, by choosing different mode parameters. We also perform direct numerical simulation to discuss the stability of local solutions. The procedure we follow provides a new method for the manipulation of spatiotemporal solitons. |
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Keywords: | Spatiotemporal accessible solitons Nonlocal nonlinear media Parabolic cylindrical coordinates |
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