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Exact solutions of the (2+1)-dimensional quintic nonlinear Schrödinger equation with variable coefficients

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Abstract

Using the self-similarity transformation, we find analytical spatial bright and dark self-similar solitons, i.e., the similaritons, of the generalized (2+1)-dimensional quintic nonlinear Schrödinger equation with varying diffraction, nonlinearity, and gain. Characteristic examples with physically relevant behavior of these similaritons are studied, and the stability of these solutions is verified with numerical integration.

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Acknowledgments

This work is supported in China by the Young teachers corporate action plan Project (XD2012358) and the National college students’ innovative entrepreneurial training program at local colleges, under Grant 201210927052, in China. Work in Qatar is supported by the NPRP 6-021-1-005 Project with the Qatar National Research Fund (a member of the Qatar Foundation). Work in Serbia has been supported by the Project OI 171006 with the Serbian Ministry of Education and Science.

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Authors and Affiliations

  1. The School of Electronic and Information Engineering, HuBei University of Science and Technology, Xianning, 437100, China

    Si-Liu Xu

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

    Nikola Petrović

  3. Science Program, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

    Milivoj R. Belić

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  1. Si-Liu Xu
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  2. Nikola Petrović
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  3. Milivoj R. Belić
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Correspondence to Si-Liu Xu.

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Xu, SL., Petrović, N. & Belić, M.R. Exact solutions of the (2+1)-dimensional quintic nonlinear Schrödinger equation with variable coefficients. Nonlinear Dyn 80, 583–589 (2015). https://doi.org/10.1007/s11071-014-1891-2

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  • DOI: https://doi.org/10.1007/s11071-014-1891-2

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