Nonlinear Dynamics

, Volume 95, Issue 2, pp 983–994 | Cite as

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

  • Chunyu Yang
  • Qin ZhouEmail author
  • Houria Triki
  • Mohammad Mirzazadeh
  • Mehmet Ekici
  • Wen-Jun LiuEmail author
  • Anjan Biswas
  • Milivoj Belic
Original Paper


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.


Variable-coefficient nonlinear Schrödinger equation Heisenberg ferromagnetic spin chain Soliton propagation Soliton interaction 



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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Information Photonics and Optical Communications, and School of ScienceBeijing University of Posts and TelecommunicationsBeijingPeople’s Republic of China
  2. 2.School of Electronics and Information EngineeringWuhan Donghu UniversityWuhanPeople’s Republic of China
  3. 3.Radiation Physics Laboratory, Department of Physics, Faculty of SciencesBadji Mokhtar UniversityAnnabaAlgeria
  4. 4.Department of Engineering Sciences, Faculty of Technology and Engineering, East of GuilanUniversity of GuilanRudsar-VajargahIran
  5. 5.Department of Mathematics, Faculty of Science and ArtsBozok UniversityYozgatTurkey
  6. 6.Department of Physics, Chemistry and MathematicsAlabama A&M UniversityNormalUSA
  7. 7.Department of Mathematics and StatisticsTshwane University of TechnologyPretoriaSouth Africa
  8. 8.Science ProgramTexas A&M University at QatarDohaQatar

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