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

Min Li, Boting Wang, Tao Xu and Lei Wang

Chaos, Solitons & Fractals, 2021, vol. 145, issue C

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.

Keywords: A general fourth-order dispersive nonlinear Schrödinger equations; Bifurcations; Travelling wave solutions; Heisenberg spin chain; Nonlinear wave excitations (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077921001193
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001193

DOI: 10.1016/j.chaos.2021.110767

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().