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Bright and dark solitons for a variable-coefficient \((2+1)\) dimensional Heisenberg ferromagnetic spin chain equation

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Abstract

Under investigation in this paper is a variable-coefficient \((2+1)\) dimensional Heisenberg ferromagnetic spin chain equation. Bilinear forms for the bright and dark soliton solutions are respectively obtained. Bright and dark solitons are obtained via the Hirota bilinear method. Features of the bright and dark solitons are discussed. Interaction properties of the bright and dark solitons are discussed via the asymptotic analysis, and stability of the bright and dark solitons is studied via the numerical calculation: (1) Amplitudes of the bright and dark solitons are not related to the coefficient \(\delta _{4}(t)\), while the soliton velocities are related to \(\delta _{4}(t)\). (2) Interactions between the bright two solitons are shown to be elastic, while interactions between the dark two solitons could be elastic or inelastic, which is determined by the values of \(\rho \). (3) Numerical calculation indicates that the bright solitons could not resist the disturbance of small perturbations, while the dark solitons could resist the disturbance of small perturbations.

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Acknowledgements

We express our sincere thanks to all the members of our discussion group for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant No. 11272023, and by the Fundamental Research Funds for the Central Universities under Grant No. 50100002016105010.

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Authors and Affiliations

  1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Qian-Min Huang, Yi-Tian Gao & Shu-Liang Jia

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  1. Qian-Min Huang
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  2. Yi-Tian Gao
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  3. Shu-Liang Jia
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Correspondence to Yi-Tian Gao.

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Huang, QM., Gao, YT. & Jia, SL. Bright and dark solitons for a variable-coefficient \((2+1)\) dimensional Heisenberg ferromagnetic spin chain equation. Opt Quant Electron 50, 183 (2018). https://doi.org/10.1007/s11082-018-1428-x

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