Dark soliton interactions for a fifth-order nonlinear Schrödinger equation in a Heisenberg ferromagnetic spin chain

• Published in: Superlattices and microstructures 2016-12, Vol.100, p.191-197
• Main Authors: Lan, Zhong-Zhou, Gao, Yi-Tian, Zhao, Chen, Yang, Jin-Wei, Su, Chuan-Qi
• Format: Article
• Language: English
• Subjects: Dark soliton interactions; Fifth-order nonlinear Schrödinger equation; Heisenberg ferromagnetic spin chain; Hirota method
• ISSN: 0749-6036; 1096-3677
• DOI: 10.1016/j.spmi.2016.09.022

Under investigation in this paper is a fifth-order nonlinear Schrödinger equation in a Heisenberg ferromagnetic spin chain. By virtue of the Hirota method with two auxiliary functions, bilinear forms, dark one-, two- and three-soliton solutions are derived. Propagation and interaction of the dark solitons are illustrated graphically: Velocities of the dark solitons are linearly related to the coefficients of the third-, fourth- and fifth-order dispersions, while amplitudes of the dark solitons do not depend on them at all. Head-on interaction between the bidirectional dark two solitons and overtaking interaction between the unidirectional dark two solitons are displayed with the different values of high-order terms, and it is shown that the shapes of the dark two solitons keep the same during the interaction. By virtue of the asymptotic analysis, we can also find interactions of the dark solitons are elastic. •By virtue of the Hirota method with two auxiliary functions, bilinear forms, dark one-, two- and three-soliton solutions are derived.•Velocities of the dark solitons are linearly related to the higher-order dispersion coefficients, while amplitudes do not depend on them at all.•Head-on and overtaking interactions between the dark two solitons are displayed, and their shapes keep the same during the interaction.