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Chin. Phys. B, 2021, Vol. 30(4): 040503    DOI: 10.1088/1674-1056/abcf9f
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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: hongli_an@njau.edu.cn   

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

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