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

doi:10.1088/1674-1056/ad8ec6

中国物理B ›› 2025, Vol. 34 ›› Issue (1): 10201-010201.doi: 10.1088/1674-1056/ad8ec6

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

Shuzhi Liu(刘树芝)¹, Ning-Yi Li(李宁逸)³, Xiaona Dong(董晓娜)², and Maohua Li(李茂华)^2,†

1 School of Statistics and Data Science, Ningbo University of Technology, Ningbo 315211, China;
2 School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China;
3 College of Wealth and Management, Ningbo University of Finance and Economics, Ningbo 315175, China

收稿日期:2024-08-30 修回日期:2024-10-12 接受日期:2024-11-05 发布日期:2024-12-06
通讯作者: Maohua Li E-mail:limaohua@nbu.edu.cn
基金资助:
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).

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

Shuzhi Liu(刘树芝)¹, Ning-Yi Li(李宁逸)³, Xiaona Dong(董晓娜)², and Maohua Li(李茂华)^2,†

1 School of Statistics and Data Science, Ningbo University of Technology, Ningbo 315211, China;
2 School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China;
3 College of Wealth and Management, Ningbo University of Finance and Economics, Ningbo 315175, China

Received:2024-08-30 Revised:2024-10-12 Accepted:2024-11-05 Published:2024-12-06
Contact: Maohua Li E-mail:limaohua@nbu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: third-order flow Gerdjikov-Ivanov equation, solitons, positons, breathers

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.

Key words: third-order flow Gerdjikov-Ivanov equation, solitons, positons, breathers

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems) 04.20.Jb (Exact solutions)

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[J]. 中国物理B, 2025, 34(1): 10201-010201.

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

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

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