|
|
Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg-de Vries equation |
Yulei Cao(曹玉雷)1, Peng-Yan Hu(胡鹏彦)2,†, Yi Cheng(程艺)3, and Jingsong He(贺劲松)1 |
1 Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China; 2 College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China; 3 School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China |
|
|
Abstract Within the (2+1)-dimensional Korteweg-de Vries equation framework, new bilinear B\"acklund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function φ(y), a family of deformed soliton and deformed breather solutions are presented with the improved Hirota's bilinear method. By choosing the appropriate parameters, their interesting dynamic behaviors are shown in three-dimensional plots. Furthermore, novel rational solutions are generated by taking the limit of the obtained solitons. Additionally, two-dimensional (2D) rogue waves (localized in both space and time) on the soliton plane are presented, we refer to them as deformed 2D rogue waves. The obtained deformed 2D rogue waves can be viewed as a 2D analog of the Peregrine soliton on soliton plane, and its evolution process is analyzed in detail. The deformed 2D rogue wave solutions are constructed successfully, which are closely related to the arbitrary function φ(y). This new idea is also applicable to other nonlinear systems.
|
Received: 12 October 2020
Revised: 29 November 2020
Accepted manuscript online: 08 December 2020
|
PACS:
|
05.45.Yv
|
(Solitons)
|
|
02.30.Jr
|
(Partial differential equations)
|
|
02.30.Ik
|
(Integrable systems)
|
|
Fund: Project supported by the National Natural Scinece Foundation of China (Grant Nos. 11671219, 11871446, 12071304, and 12071451). |
Corresponding Authors:
†Corresponding author. E-mail: pyhu@szu.edu.cn
|
Cite this article:
Yulei Cao(曹玉雷), Peng-Yan Hu(胡鹏彦), Yi Cheng(程艺), and Jingsong He(贺劲松) Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg-de Vries equation 2021 Chin. Phys. B 30 030503
|
1 Akhmediev N, Ankiewicz A and Taki M 2009 Phys. Lett. A 373 675 2 Peregrine D H 1983 J. Aust. Math. Soc. B 25 16 3 Guo L J, Wang L H, Cheng Y and He J S 2017 Commun. Nonlinear Sci. Numer. Simulat. 52 11 4 Zhang Y S, Guo L J, Chabchoub A and He J S 2017 Rom. J. Phys. 62 102 5 Zhang G Q and Yan Z Y 2018 Commun. Nonlinear Sci. Numer. Simulat. 62 117 6 He J S, Xu S W and Porsezian K 2012 Phys. Rev. E 86 066603 7 Li R M, Geng X G and Xue B 2020 J. Nonlinear Math. Phys. 27 279 8 Yang J and Zhu Z N 2018 Chaos 28 093103 9 Ling L M, Feng B F and Zhu Z N 2016 Physica D 327 13 10 Cao Y L, He J S, Cheng Y and Mihalache D 2020 Nonlinear Dyn. 99 3013 11 Gai L T, Ma W X and Li M C 2020 Phys. Lett. A 384 126178 12 Rao J G, Zhang Y S, Fokas A S and He J S 2018 Nonlinerity 31 4090 13 Liu W H, Zhang Y F and Shi D D 2019 Phys. Lett. A 383 97 14 Rao J G, Wang L H, Liu W and He J S 2017 Theor. Math. Phys. 193 1783 15 Cao Y L, Malomed B A and He J S 2018 Chaos Soliton. Fract. 114 99 16 Ohta Y and Yang J K 2013 J. Phys. A: Math. Theor. 46 105202 17 Rao J G, Mihalache D, Cheng Y and He J S 2019 Phys. Lett. A 383 1138 18 Zhang Y S, Rao J G, Porsezian K and He J S 2019 Nonlinear Dyn. 95 1133 19 Elawady E and Moslem W M 2011 Phys. Plasmas 18 082306 20 Bailung H, Sharma S K and Nakamura Y 2011 Phys. Rev. Lett. 107 255005 21 Bludov Y V, Konotop V V and Akhmediev N 2009 Phys. Rev. A 80 2962 22 Bludov Y V, Konotop V V and Akhmediev N 2010 Eur. Phys. J. Spec. Top. 185 169 23 Stenflo L and Marklund M 2010 J. Plasma Phys. 76 293 24 Montina A, Bortolozzo U, Residori S and Arecchi F T 2009 Phys. Rev. Lett. 103 173901 25 Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 1054 26 Mihalache D 2017 Rom. Rep. Phys. 69 403 27 Ganshin A N, Efimov V B, Kolmakov G V, Mezhov-Deglin L P and Mcclintock P V E 2008 Phys. Rev. Lett. 101 065303 28 Guo L J, He J S, Wang L H, Cheng Y, Frantzeskakis D J, Bremer T S and Kevrekidis P G 2020 Phys. Rev. Research 2 033376 29 Boiti M, Leon J J P, Manna M and Pempinelli F 1986 Inverse Probl. 2 271 30 Lou S Y and Hu X B 1997 J. Math. Phys. 38 6401 31 Estevez P G and Leble S 1995 Inverse Probl. 11 925 32 Leble S B and Ustinov N V 1991 Inverse Probl. 10 617 33 Hirota R and Satsma J 1994 J. Phys. Soc. Jpn. 40 611 34 Ablowitz M J and Clarkson P A1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press) 35 Delisle L and Mosaddeghi M 2013 J. Phys. A: Math. Theor. 46 115203 36 Lue X, Tian B, Sun K and Wang P 2010 J. Math. Phys. 51 113506 37 Luo L 2011 Phys. Lett. A 375 1059 38 Wang C J 2017 Nonlinear Dyn. 87 2635 39 Clarkson P A and Mansfield E L 1994 Nonlinearity 7 795 40 Tian B and Gao Y T 1996 Chaos Soliton Fract. 7 1497 41 Lou S Y 1995 J. Phys. A: Math. Theor. 28 7227 42 Hu H C, Tang X Y, Lou S Y and Liu Q P 2004 Chaos Soliton Fract. 22 327 43 Chen Y, Wang Q and Li B 2004 Commun. Theor. Phys. 42 655 44 Fan E G 2009 J. Phys. A: Math. Theor. 42 095206 45 Luo L 2010 Commun. Theor. Phys. 54 208 46 Chen Y R, Song M and Liu Z R 2015 Nonlinear Dyn. 82 333 47 Liu Y Q and Wen X Y 2019 Adv. Diff. Equa. 2019 332 48 Wang C J 2016 Nonlinear Dyn. 84 697 49 Gilson C, Lambert F, Nimmo J and Willox R 1996 Proc. Roy. Soc. Lond. A 452 223 50 Bell E T 1935 Ann. Math. 35 258 51 Fan E G 2011 Phys. Lett. A 375 493 52 Luo L 2019 Appl. Math. Lett. 94 94 53 Lambert F and Springael J 2001 Chaos Soliton Fract. 12 2821 54 Hirota R2004 The direct method in soliton theory (Cambridge: Cambridge University Press) 55 Ablowitz M J and Satsuma J 1979 J. Math. Phys. 20 1496 |
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
|
|
|