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Bright soliton interactions in a \(\mathbf (2 +\mathbf 1) \)-dimensional fourth-order variable-coefficient nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin chain

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Abstract

Interactions of bright solitons in the Heisenberg ferromagnetic spin chain, governed by a \((2+1)\)-dimensional nonlinear Schrödinger equation with variable coefficients, are investigated theoretically. Analytical soliton solutions are derived by means of the Hirota bilinear method. Different scenarios of soliton propagation and interactions are illustrated. The influence of relevant parameters and variable coefficients of different function types on the soliton propagation and interactions is discussed. Solitons of different shapes in propagation, whose pulse widths and oscillation periods vary with the phase shift, are presented. The method for controlling the size of the phase shift is proposed. Furthermore, the fission solitons and the bound solitons, produced after their collisions, are displayed. Methods for controlling the number and amplitudes of fission solitons, the distance between solitons and the intensity of their interactions are put forward. Results in this paper will contribute to the effective control of solitons in the Heisenberg ferromagnetic spin chain system.

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Acknowledgements

The work of Qin Zhou was supported by the National Natural Science Foundation of China (Grant Nos. 11705130 and 1157149) and by the Chutian Scholar Program of Hubei Government in China. The work of Wenjun Liu was supported by the National Natural Science Foundation of China (Grant Nos. 11674036 and 11875008), by the Beijing Youth Top-notch Talent Support Program (Grant No. 2017000026833ZK08), and by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, Grant Nos. IPOC2016ZT04 and IPOC2017ZZ05). The research work of Milivoj Belic was supported by the Qatar National Research Fund (QNRF) under the Grant Number NPRP 8-028-1-001.

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Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing, 100876, People’s Republic of China

    Chunyu Yang & Wen-Jun Liu

  2. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, People’s Republic of China

    Qin Zhou

  3. Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P. O. Box 12, 23000, Annaba, Algeria

    Houria Triki

  4. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, 44891-63157, Iran

    Mohammad Mirzazadeh

  5. Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100, Yozgat, Turkey

    Mehmet Ekici

  6. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL, 35762, USA

    Anjan Biswas

  7. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, 0008, South Africa

    Anjan Biswas

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

    Milivoj Belic

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  1. Chunyu Yang
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  2. Qin Zhou
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Yang, C., Zhou, Q., Triki, H. et al. Bright soliton interactions in a \(\mathbf (2 +\mathbf 1) \)-dimensional fourth-order variable-coefficient nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin chain. Nonlinear Dyn 95, 983–994 (2019). https://doi.org/10.1007/s11071-018-4609-z

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