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Shuzhi Liu(刘树芝), Ning-Yi Li(李宁逸), Xiaona Dong(董晓娜), and Maohua Li(李茂华). 2025: Darboux transformation, positon solution, and breather solution of the third-order flow Gerdjikov-Ivanov equation, Chinese Physics B, 34(1): 010201. doi: 10.1088/1674-1056/ad8ec6

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Shuzhi Liu(刘树芝), Ning-Yi Li(李宁逸), Xiaona Dong(董晓娜), and Maohua Li(李茂华). 2025: Darboux transformation, positon solution, and breather solution of the third-order flow Gerdjikov-Ivanov equation, Chinese Physics B, 34(1): 010201. doi: 10.1088/1674-1056/ad8ec6

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

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 Date: 30/08/2024
Accepted Date: 12/10/2024
Fund Project:
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).

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.
- third-order flow Gerdjikov-Ivanov equation,
- solitons,
- positons,
- breathers

References

Russell J S 1844 Report on Waves. Report of the 14th Meeting of the British Association for the Advancement of Science (London)

Google Scholar Pub Med

Korteweg D J and de Vries G 1895 Philos. Mag. 39 422

Google Scholar Pub Med

Gardner C S and Morikawa G K 1960 Similarity in the asymptotic behavior of collision-free hydromagnetic waves and water waves (New York University)

Google Scholar Pub Med

Kruskal M D 1965 Proceedings of the IBM Scientific Computing Symposium on Large-Scale Problems in Physics (White Plains, New York)

Google Scholar Pub Med

Hasegawa A and Tappert F 1973 Appl. Phys. Lett. 23 142

Google Scholar Pub Med

Hirota R 1973 J. Math. Phys. 14 805

Google Scholar Pub Med

Kundu A 1984 J. Math. Phys. 25 3433

Google Scholar Pub Med

Wang X, Yang B, Chen Y and Yang Y Q 2014 Phys. Scr. 89 095210

Google Scholar Pub Med

Kruglov V I, Peacock A C and Harvey J D 2003 Phys. Rev. Lett. 90 113902

Google Scholar Pub Med

Wang L H, Porsezian K and He J S 2013 Phys. Rev. E 87 053202

Google Scholar Pub Med

Xu SW, He J S andWang L H 2011 J. Phys. A-Math. Theor. 44 305203

Google Scholar Pub Med

Zhang Y S, Guo L J, Xu S W, Wu Z W and He J S 2014 Commun. Nonlinear Sci. Numer. Simul. 19 1706

Google Scholar Pub Med

Zhang H Q, Liu R and Chen F 2023 Nonlinear Dyn. 111 645

Google Scholar Pub Med

Xiang Y J, Dai X Y, Wen S C, Guo J and Fan D Y 2011 Phys. Rev. A 84 033815

Google Scholar Pub Med

Kaup D J and Newell A C 1978 J. Math. Phys. 19 798

Google Scholar Pub Med

Chen H H, Lee Y C and Liu C S 1979 Phys. Scr. 20 490

Google Scholar Pub Med

Gerdjikov V S and Ivanov M I 1983 Bulg. J. Phys. 10 130

Google Scholar Pub Med

Mjølhus E 1976 J. Plasma Phys. 16 321

Google Scholar Pub Med

Mjølhus E 1989 Phys. Scr. 40 227

Google Scholar Pub Med

Agrawal G P 2000 Nonlinear fiber optics. Nonlinear Science at the Dawn of the 21st Century 542 195

Google Scholar Pub Med

Zhu J Y and Chen Y 2024 Acta Math. Appl. Sin-E. 40 358

Google Scholar Pub Med

Li Y S, Gu X S and Zou M R 1987 Acta Math. Sin. (New Series) 3 143

Google Scholar Pub Med

Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)

Google Scholar Pub Med

Gu C H, Hu H S and Zhou Z X 2006 Darboux Trasformations in Integrable Systems (Dortrecht: Springer)

Google Scholar Pub Med

He J S, Zhang L, Cheng Y and Li Y S 2006 Sci. China Ser. A Math. 49 1867

Google Scholar Pub Med

Liu J Z, Yan X X, Jin M and Xin X P 2023 Chin. Phys. B 32 120401

Google Scholar Pub Med

Wei J, Geng X G and Wang X 2024 Chin. Phys. B 33 070202

Google Scholar Pub Med

Matveev V B 1992 Phys. Lett. A 166 205

Google Scholar Pub Med

Maisch H and Stahlhofen A A 1995 Phys. Scr. 52 228

Google Scholar Pub Med

Hu H C and Liu Y 2008 Phys. Lett. A 372 5795

Google Scholar Pub Med

Song W J, Xu S W, Li M H and He J S 2019 Nonlinear Dyn. 97 2135

Google Scholar Pub Med

Yuan F and Ghanbari B 2023 Chin. Phys. B 32 075208

Google Scholar Pub Med

Wadati M 1973 J. Phys. Soc. Jpn. 34 1289

Google Scholar Pub Med

Xu S W and He J S 2012 J. Math. Phys. 53 063507

Google Scholar Pub Med

Lin H A, He J S,Wang L H and Mihalache D 2020 Nonlinear Dyn. 100 2839

Google Scholar Pub Med

Yang X, Zhang Z and Li B 2020 Chin. Phys. B 29 100501

Google Scholar Pub Med

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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

Received Date: 30/08/2024

Accepted Date: 12/10/2024

Fund Project:

Key words:

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.

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

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

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