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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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.
KeywordsVariable-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.
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Conflict of interest
The authors declare that they have no conflict of interest.
- 17.Liu, W.J., Liu, M.L., Lei, M., Fang, S.B., Wei, Z.Y.: Titanium selenide saturable absorber mirror for passive Q-switched Er-doped fiber laser. IEEE J. Sel. Top. Quant. 24, 0901005 (2018)Google Scholar
- 38.Wang, Q.M., Gao, Y.T., Su, C.Q., Mao, B.Q., Gao, Z., Yang, J.W.: Dark solitonic interaction and conservation laws for a higher-order \((2+1)\)-dimensional nonlinear Schrödinger-type equation in a Heisenberg ferromagnetic spin chain with bilinear and biquadratic interaction. Ann. Phys. 363, 440–456 (2015)CrossRefzbMATHGoogle Scholar
- 46.Yang, J.W., Gao, Y.T., Wang, Q.M., Su, C.Q., Feng, Y.J., Yu, X.: Bilinear forms and soliton solutions for a fourth-order variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain or an alpha helical protein. Physica B 481, 148–155 (2016)CrossRefGoogle Scholar
- 47.Zhao, X.H., Tian, B., Liu, D.Y., Wu, X.Y.: Dark solitons, Lax pair and infinitely-many conservation laws for a generalized \((2+1)\)-dimensional variable-coefficient nonlinear Schröodinger equation in the inhomogeneous Heisenberg ferromagnetic spin chain. Mod. Phys. Lett. B 31, 1750013 (2017)CrossRefGoogle Scholar