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Quantitative analysis on the bifurcations and exact travelling wave solutions of a generalized fourth-order dispersive nonlinear Schrödinger equation in Heisenberg spin chain

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  • Li, Min
  • Wang, Boting
  • Xu, Tao
  • Wang, Lei

Abstract

In this paper, we analyzed the bifurcations and travelling wave solutions of a general fourth-order dispersive nonlinear Schrödinger equation arising in one dimension Heisenberg spin chain with twist interaction. First of all, based on the bifurcation theory of planar dynamical system, we obtained six types of phase portraits in the (x,y)-plane under different parametric conditions and revealed qualitatively the existence of the bright solitary wave, dark solitary wave, periodic wave, periodic breaking wave and unbounded wave solutions. Furthermore, we established the quantitative correspondence between the phase orbits and the energy level h. Finally, we derived the travelling wave solutions corresponding to the phase trajectories, which are found to be entirely consistent with the qualitative analysis on the types of solutions. Our results can be more easily applied to model the nonlinear wave excitations in the Heisenberg ferromagnetic spin chains with twist interactions.

Suggested Citation

  • Li, Min & Wang, Boting & Xu, Tao & Wang, Lei, 2021. "Quantitative analysis on the bifurcations and exact travelling wave solutions of a generalized fourth-order dispersive nonlinear Schrödinger equation in Heisenberg spin chain," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001193
    DOI: 10.1016/j.chaos.2021.110767
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    References listed on IDEAS

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    1. Daniel, M. & Beula, J., 2009. "Soliton spin excitations in a Heisenberg helimagnet," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1842-1848.
    2. Hai-Qiang Zhang & Bo Tian & Xiang-Hua Meng & Xing Lü & Wen-Jun Liu, 2009. "Conservation laws, soliton solutions and modulational instability for the higher-order dispersive nonlinear Schrödinger equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(2), pages 233-239, November.
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    Cited by:

    1. Acharya, S.P. & Janaki, M.S., 2022. "Nonlinear dynamical modelling of high frequency electrostatic drift waves using fluid theoretical approach in magnetized plasma," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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