Darboux transformation, positon solution, and breather solution of the third-order flow Gerdjikov-Ivanov equation

doi:10.1088/1674-1056/ad8ec6

Abstract The third-order flow Gerdjikov-Ivanov (TOFGI) equation is studied, and the Darboux transformation (DT) is used to obtain the determinant expression of the solution of this equation. On this basis, the soliton solution, rational solution, positon solution, and breather solution of the TOFGI equation are obtained by taking zero seed solution and non-zero seed solution. The exact solutions and dynamic properties of the Gerdjikov-Ivanov (GI) equation and the TOFGI equation are compared in detail under the same conditions, and it is found that there are some differences in the velocities and trajectories of the solutions of the two equations.

Keywords: third-order flow Gerdjikov-Ivanov equation solitons positons breathers

Received: 30 August 2024
Revised: 12 October 2024
Accepted manuscript online: 05 November 2024

PACS:	02.30.Jr	(Partial differential equations)
	02.30.Ik	(Integrable systems)
	04.20.Jb	(Exact solutions)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12201329), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY24A010002), and the Natural Science Foundation of Ningbo (Grant No. 2023J126).

Corresponding Authors: Maohua Li
E-mail: limaohua@nbu.edu.cn

Cite this article:

Shuzhi Liu(刘树芝), Ning-Yi Li(李宁逸), Xiaona Dong(董晓娜), and Maohua Li(李茂华) Darboux transformation, positon solution, and breather solution of the third-order flow Gerdjikov-Ivanov equation 2025 Chin. Phys. B 34 010201

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Darboux transformation, positon solution, and breather solution of the third-order flow Gerdjikov-Ivanov equation

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