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Nonlinear Dynamics

, Volume 87, Issue 2, pp 827–834 | Cite as

Spatiotemporal soliton clusters in strongly nonlocal media with variable potential coefficients

  • Si-Liu Xu
  • Li Xue
  • Milivoj R. Belić
  • Jun-Rong He
Original Paper

Abstract

We study analytically and numerically spatiotemporal solitons in three-dimensional strongly nonlocal nonlinear media. A broad class of exact self-similar solutions to the strongly nonlocal Schrödinger equation with variable potential coefficients has been obtained. We find robust soliton cluster solutions of the accessible type, constructed with the help of Kummer and Hermite functions. They are characterized by the set of three quantum numbers. Dynamical features of these spatiotemporal accessible solitons are discussed. The validity of the analytical solutions and their stability is verified by means of direct numerical simulations.

Keywords

Light bullet Strongly nonlocal nonlinear Nonlinear Schrödinger equation 

Notes

Acknowledgments

This work is supported in China by the Department of Science of Hubei Province of China (Grant Nos. 2015CFC779, 2013CFC011), the National Natural Science Foundation of China (61340042) and the Educational Commission of Hubei Province of China (Grant No. D20142803). In addition, work in Qatar is supported by the NPRP 6-021-1-005 Project with the Qatar National Research Fund and in China by the Natural Science Foundation of Guangdong Province under Grant No. 1015283001000000. MRB also acknowledges Al Sraiya Holding Group in Qatar, for additional support.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Si-Liu Xu
    • 1
  • Li Xue
    • 1
  • Milivoj R. Belić
    • 2
    • 3
  • Jun-Rong He
    • 1
  1. 1.The School of Electronic and Information EngineeringHuBei University of Science and TechnologyXianningChina
  2. 2.Texas A&M University at QatarDohaQatar
  3. 3.Institute of PhysicsUniversity of BelgradeBelgradeSerbia

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