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An exact (2 + 1)-dimensional optical soliton with spatially modulated nonlinearity and an external potential

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Abstract

An exact (2 + 1)-dimensional spatial optical soliton of the nonlinear Schrödinger equation with a spatially modulated nonlinearity and a special external potential is discovered in an inhomogeneous nonlinear medium, by utilizing the similarity transformation. Exact analytical solutions are constructed by the products of Whittaker functions and the bright and dark soliton solutions of the standard stationary nonlinear Schrödinger equation. Some examples of such composed solutions are given, in which these spatial solitons display different localized structures. Numerical calculation shows that the soliton is stable in propagating over long distances, thus also confirming the validity of the exact solution.

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Authors and Affiliations

  1. Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde, 528300, P.R. China

    Wei-Ping Zhong

  2. Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

    Wei-Ping Zhong & Milivoj Belić

  3. Institute of Physics, University of Belgrade, P.O. Box 68, 11001, Belgrade, Serbia

    Milivoj Belić

Authors
  1. Wei-Ping Zhong
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  2. Milivoj Belić
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Correspondence to Wei-Ping Zhong.

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Zhong, WP., Belić, M. An exact (2 + 1)-dimensional optical soliton with spatially modulated nonlinearity and an external potential. Eur. Phys. J. D 68, 331 (2014). https://doi.org/10.1140/epjd/e2014-50580-9

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  • DOI: https://doi.org/10.1140/epjd/e2014-50580-9

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