Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(4): 040503    DOI: 10.1088/1674-1056/abcf9f
GENERAL Prev   Next  

General M-lumps, T-breathers, and hybrid solutions to (2+1)-dimensional generalized KDKK equation

Peisen Yuan(袁培森)1, Jiaxin Qi(齐家馨)3, Ziliang Li(李子良)2, and Hongli An(安红利)3,†
1 College of Artificial Intelligence, Nanjing Agricultural University, Nanjing 210095, China; 2 College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao 266100, China; 3 College of Sciences, Nanjing Agricultural University, Nanjing 210095, China
Abstract  A special transformation is introduced and thereby leads to the N-soliton solution of the (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (KDKK) equation. Then, by employing the long wave limit and imposing complex conjugate constraints to the related solitons, various localized interaction solutions are constructed, including the general M-lumps, T-breathers, and hybrid wave solutions. Dynamical behaviors of these solutions are investigated analytically and graphically. The solutions obtained are very helpful in studying the interaction phenomena of nonlinear localized waves. Therefore, we hope these results can provide some theoretical guidance to the experts in oceanography, atmospheric science, and weather forecasting.
Keywords:  KDKK equation      Hirota bilinear method      high-order lump solution      T-breather solution      hybrid solution  
Received:  20 October 2020      Revised:  22 November 2020      Accepted manuscript online:  02 December 2020
PACS:  05.45.Yv (Solitons)  
  02.30.Ik (Integrable systems)  
  02.30.Jr (Partial differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11775116) and the Jiangsu Qinglan High-Level Talent Project.
Corresponding Authors:  Corresponding author. E-mail:   

Cite this article: 

Peisen Yuan(袁培森), Jiaxin Qi(齐家馨), Ziliang Li(李子良), and Hongli An(安红利) General M-lumps, T-breathers, and hybrid solutions to (2+1)-dimensional generalized KDKK equation 2021 Chin. Phys. B 30 040503

1 Ablowitz M A and Clarkson P A 1991 Soliton, Nonlinear Evolution Equations and Inverse Scatting (NewYork: Cambridge University Press)
2 Rogers C and Schief W K 2002 Bäcklund and Darboux Transformations Geometry and Modern Applications in Soliton Theory (NewYork: Cambridge University Press)
3 Hirota R 2004 The Direct Method in Soliton Theory (NewYork: Cambridge University Press)
4 Hu X B 1993 J. Phys. A: Math. Gen. 26 L465
5 Cao C W, Wu Y T and Geng X G 1999 J. Math. Phys. 40 3948
6 Liu Q P and Manas M 2000 Phys. Lett. B 485 293
7 Ma W X and Fuchssteiner B 1996 Int. J. Nonlinear Mech. 31 329
8 Ma W X and You Y C 2005 Trans. Amer. Math. Soc. 357 1753
9 Lou S Y and Lu J Z 1996 J. Phys. A: Math. Gen. 29 4209
10 Fan E G 2000 Phys. Lett. A 277 212
11 Yan Z Y 2001 Phys. Lett. A 292 100
12 Chen Y and Wang Q 2006 J. Appl. Math. Comput. 177 396
13 Ma W X 2005 Nonlinear Analysis 63 e2461
14 Trogdon T and Deconinck B 2013 Appl. Math. Lett. 26 5
15 Zhao P and Fan E G 2020 Physica D 402 132213
16 Tian S F 2017 J. Diff. Equ. 262 506
17 Wang D S, Guo B L and Wang X L 2019 J. Diff. Equ. 266 5209
18 Tajiri M and Arai T 1999 Phys. Rev. E 60 2297
19 Akhmediev N, Soto-Crespo J and Ankiewicz A 2009 Phys. Rev. A 80 043818
20 Kedziora D J, Ankiewicz A and Akhmediev N 2012 Phys. Rev. E 85 066601
21 He J S, Zhang H R, Wang L H and Fokas A S 2013 Phys. Rev. E 87 052914
22 Yue Y F, Huang L L and Chen Y 2018 Comput. Math. Appl. 75 2538
23 Wang X B, Tian S F, Qin C Y and Zhang T T 2017 Appl. Math. Lett. 68 40
24 Liu Y Q, Wen X Y and Wang D S 2019 Comput. Math. Appl. 78 1
25 Zhang H Q and Ma W X 2017 Nonlinear Dyn. 87 2305
26 Zhang X E, Chen Y and Zhang Y 2017 Comput. Math. Appl. 74 2341
27 Yong X L, Ma W X, Huang Y H and Liu Y 2018 Comput. Math. Appl. 75 3414
28 Huang L L, Yue Y F and Chen Y 2018 Comput. Math. Appl. 74 831
29 Wang H F and Zhang Y F 2020 Chin. Phys. B 29 040501
30 Ma W X, Zhang Y and Tang Y N 2020 East Asian J. Appl. Math. 10 732
31 Yang J Y, Ma W X and Khalique C M 2020 Eur. Phys. J. Plus. 135 494
32 Ma W X and Zhang L Q 2020 Pramana-J. Phys. 94 43
33 Ma W X 2015 Phys. Lett. A 379 1975
34 Lü X, Chen S T and Ma W X 2006 Nonlinear Dyn. 86 523
35 Wang J, An H L and Li B 2019 Mod. Phys. Lett. B 33 1950262
36 Yang J Y, Ma W X and Qin Z Y 2017 Anal. Math. Phys. 8 427
37 Yang J Y and Ma W X 2017 Comput. Math. Appl. 73 220
38 Wen X Y and Wang H T 2020 Acta Phys. Sin. 69 010205 (in Chinese)
39 Whitham G B 1974 Linear and Nonlinear Waves(New York: John Wiley & Sons)
40 Kundu P K 1990 Fluid Mechanics (San Diego: Academic Press)
41 Lamb H1945 Hydrodynamics (Cambridge: Cambridge University Press)
42 Lan Z, Gao Y, Yang J W, Su C Q and Wang Q 2016 Mod. Phys. Lett. B 30 1650265
43 Yang X, Fan R and Li B 2020 Phys. Scr. 95 045213
44 Peng W Q, Tian S F and Zhang T T 2018 Phys. Lett. A 382 2701
45 Feng L L, Tian S F, Wang X B and Zhang T T 2019 Frontiers of Mathematics in China 14 631
46 Lü X and Li J 2014 Nonlinear Dyn. 77 135
47 Xin X P, Liu X Q and Zhang L L 2010 Appl. Math. Comput. 215 3669
48 Satsuma J and Ablowitz M J 1979 J. Math. Phys. 20 1496
[1] Propagation and modulational instability of Rossby waves in stratified fluids
Xiao-Qian Yang(杨晓倩), En-Gui Fan(范恩贵), and Ning Zhang(张宁). Chin. Phys. B, 2022, 31(7): 070202.
[2] Solutions of novel soliton molecules and their interactions of (2 + 1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation
Hong-Cai Ma(马红彩), Yi-Dan Gao(高一丹), and Ai-Ping Deng(邓爱平). Chin. Phys. B, 2022, 31(7): 070201.
[3] High-order rational solutions and resonance solutions for a (3+1)-dimensional Kudryashov-Sinelshchikov equation
Yun-Fei Yue(岳云飞), Jin Lin(林机), and Yong Chen(陈勇). Chin. Phys. B, 2021, 30(1): 010202.
[4] Interaction properties of solitons for a couple of nonlinear evolution equations
Syed Tahir Raza Rizvi, Ishrat Bibi, Muhammad Younis, and Ahmet Bekir. Chin. Phys. B, 2021, 30(1): 010502.
[5] Stable soliton propagation in a coupled (2+1) dimensional Ginzburg-Landau system
Li-Li Wang(王丽丽), Wen-Jun Liu(刘文军). Chin. Phys. B, 2020, 29(7): 070502.
[6] Localized characteristics of lump and interaction solutions to two extended Jimbo-Miwa equations
Yu-Hang Yin(尹宇航), Si-Jia Chen(陈思佳), and Xing Lü(吕兴). Chin. Phys. B, 2020, 29(12): 120502.
[7] Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev-Petviashvili equation
Zhao Zhang(张钊), Xiangyu Yang(杨翔宇), Wentao Li(李文涛), Biao Li(李彪). Chin. Phys. B, 2019, 28(11): 110201.
[8] Exact solutions of a (2+1)-dimensional extended shallow water wave equation
Feng Yuan(袁丰), Jing-Song He(贺劲松), Yi Cheng(程艺). Chin. Phys. B, 2019, 28(10): 100202.
[9] Superposition solitons in two-component Bose-Einstein condensates
Wang Xiao-Min (王晓敏), Li Qiu-Yan (李秋艳), Li Zai-Dong (李再东). Chin. Phys. B, 2013, 22(5): 050311.
[10] Periodic-soliton solutions of the (2+1)-dimensional Kadomtsev--Petviashvili equation
Zhaqilao(扎其劳) and Li Zhi-Bin(李志斌). Chin. Phys. B, 2008, 17(7): 2333-2338.
No Suggested Reading articles found!