|
|
|
From breather solutions to lump solutions: A construction method for the Zakharov equation |
| Feng Yuan(袁丰)1,†, Behzad Ghanbari2, Yongshuai Zhang(张永帅)3, and Abdul Majid Wazwaz4 |
1 College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Department of Mathematics, Kermanshah University of Technology, Kermanshah, Iran;
3 Department of Mathematics, Shaoxing University, Shaoxing 312000, China;
4 Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA |
|
|
|
|
Abstract Periodic solutions of the Zakharov equation are investigated. By performing the limit operation λ2l-1 to λ1 on the eigenvalues of the Lax pair obtained from the n-fold Darboux transformation, an order-n breather-positon solution is first obtained from a plane wave seed. It is then proven that an order-n lump solution can be further constructed by taking the limit λ1 to λ0 on the breather-positon solution, because the unique eigenvalue λ0 associated with the Lax pair eigenfunction Ψ(λ0)=0 corresponds to the limit of the infinite-periodic solutions. A convenient procedure of generating higher-order lump solutions of the Zakharov equation is also investigated based on the idea of the degeneration of double eigenvalues in multi-breather solutions.
|
Received: 16 July 2023
Revised: 23 August 2023
Accepted manuscript online: 06 September 2023
|
|
PACS:
|
02.30.Ik
|
(Integrable systems)
|
| |
02.30.Jr
|
(Partial differential equations)
|
| |
05.45.-a
|
(Nonlinear dynamics and chaos)
|
|
| Fund: This work is sponsored by NUPTSF (Grant Nos.NY220161 and NY222169), the Foundation of Jiangsu Provincial Double-Innovation Doctor Program (Grant No.JSSCBS20210541), the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No.22KJB110004), and the National Natural Science Foundation of China (Grant No.12171433). |
Corresponding Authors:
Feng Yuan
E-mail: yf2017@mail.ustc.edu.cn
|
Cite this article:
Feng Yuan(袁丰), Behzad Ghanbari, Yongshuai Zhang(张永帅), and Abdul Majid Wazwaz From breather solutions to lump solutions: A construction method for the Zakharov equation 2023 Chin. Phys. B 32 120201
|
[1] Hasegawa A and Tappert F 1972 Appl. Phys. Lett. 23 142
[2] Hasegawa A and Tappert F 1973 Appl. Phys. Lett. 23 171
[3] Maneuf S, Desailly R and Froehly C 1988 Opt. Commun. 65 193
[4] Mollenauer L F, Stolen R H and Gordon J P 1980 Phys. Rev. Lett. 45 1095
[5] Kedziora D J, Ankiewicz A and Akhmediev N 2011 Phys. Rev. E 84 056611
[6] Guo B L, Ling L M and Liu Q P 2012 Phys. Rev. E 85 026607
[7] Ohta Y and Yang J K 2012 Proc. R. Soc. A 468 1716
[8] Kedziora D J, Ankiewicz A and Akhmediev N 2013 Phys. Rev. E 88 013207
[9] Wang L H, He J S, et al. 2017 Phys. Rev. E 95 042217
[10] Davey A and Stewartson K 1974 Proc. R Soc. Lond. A 338 101
[11] Panguetna C S, Tabi C B and Kofané T C 2017 Phys. Plasmas 24 092114
[12] Leblond H 2005 Phys. Rev. Lett. 95 033902
[13] Ablowitz M J and Segur H 1979 J. Fluid Mech. 92 691
[14] Fokas A S and Santini P M 1989 Phys. Rev. Lett. 63 1329
[15] Ohta Y and Yang J K 2012 Phys. Rev. E 86 036604
[16] Rao J G, Fokas A S and He J S 2021 J. Nonlinear Sci. 31 67
[17] Guo L J, He J S, Wang L H, et al. 2020 Phys. Rev. Res. 2 033376
[18] Guo L J, Chen L, Mihalache D and He J S 2022 Phys. Rev. E 105 014218
[19] Guo L J, Keverkidis P G and He J S 2022 J. Phys. A: Math. Theo. 55 475701
[20] Zakharov V E 1980 The Inverse Scattering Method. In: Bullough R K and Caudrey P J (eds) Solitons. Topics in Current Physics (Berlin: Springer) Vol. 17 pp 243--285
[21] Strachan I A B 1992 J. Math. Phys. 33 2477
[22] Strachan I A B 1993 J. Math. Phys. 34 243
[23] Radha R and Lakshmanan M 1994 Inverse Problems 10 L29
[24] Estevez P G and Hernáez G A 1999 arXiv: solv-int/9910005v1
[25] Myrzakulov R, Vijayalakshmi S, et al. 1997 Phys. Lett. A 233 391
[26] Velan M S and Lakshmanan M 1998 J. Nonlinear Math. Phys. 5 190
[27] Strachan I A B 1992 Inverse Problems 8 L21
[28] Hosseini K, Sadri K, Salahshour S, et al. 2021 Optik 229 166247
[29] Zhang H Q, Li L L and Xue Y S 2009 Physica A 388 9
[30] Yuan F 2022 Roman. Rep. Phys. 74 121
[31] Younis M, Cheemaa N, Mehmood S A, et al. 2020 Waves in Random and Complex Media 30 490
[32] Liu C F and Wang Z P 2015 Int. J. Numer. Methods Heat Fluid Flow 25 656
[33] Liu C F, Chen M, Zhou P and Chen L W 2016 J. Appl. Anal. Comput. 6 367
[34] Rao J G, Wang L H, Liu W, et al. 2017 Theor. Math. Phys. 193 1783
[35] Wang X B, Tian S F and Zhang T T 2018 Proc. Am. Math. Soc. 146 3353
[36] Chen Y, Wang X B and Han B 2020 Mod. Phys. Lett. B 34 2050234
[37] Radha R and Lakshmanan M 1997 J. Phys. A: Math. Gen. 30 3229
[38] Petviashvili V I 1976 Plasma Phys. 2 469
[39] Ablowitz M J and Satsuma J 1978 J. Math. Phys. 19 2180
[40] Villarroel J and Ablowitz M J 1999 Commun. Math. Phys. 207 1
[41] Jorge M C M, Pacheco G C, et al. 2005 Chaos 15 037104
[42] Ma W X 2015 Phys. Lett. A 379 1975
[43] Wang H 2018 Appl. Math. Lett. 85 27
[44] Ma W X and Zhou Y 2018 J. Different. Equ. 264 2633
[45] Rao J G, He J S and Malomed B A 2022 J. Math. Phys. 63 013510
[46] Stepanyants Y, Zakharov D and Zakharov V 2022 Radiophys. Quantum Electron. 64 665
[47] Guo L J, Wang L H, Chen L and He J S 2023 Stud. Appl. Math. 151 35
[48] Xing Q X, Wang L H, Mihalache D, Porsezian K and He J S 2017 Chaos 27 053102
[49] Qiu D Q and Cheng W G 2019 Appl. Math. Lett. 98 13
[50] Yuan F 2021 Int. J. Mod. Phys. B 35 2150053 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
