Dynamics of multi-breathers, N-solitons and M-lump solutions in the (2+1)-dimensional KdV equation

  • Wei TanEmail author
  • Zheng-De Dai
  • Zhao-Yang Yin
Original Paper


The (2+1)-dimensional Korteweg–de Vries (KdV) equation is studied by distinct methods. The parameter limit method is used to derive multi-breathers solutions and lump solutions with different structures. The Hirota’s bilinear method is used to obtain N-soliton solutions, N-order rational solutions and M-lump solutions. Besides, we also analyze parametric reasons for the degradation of breathers solutions and emergence of different lump solutions, and simulate the different structures of the exact solutions obtained in this paper by using three-dimensional images.


(2+1)-Dimensional KdV equation Breather waves Lump solutions Solitary waves Hirota’s bilinear method 



The authors would like to express their sincere thanks to the referees for their enthusiastic guidance and help. This work was supported by the National Natural Science Foundation of P.R. China No. 11661037, Scientific Research Project of Hunan Education Department No.17C1297, Jishou University Natural Science Foundation No. Jd1801 and laboratory open Foundation No.JDLF2018041.

Author Contributions

The authors declare that the study was realized in collaboration with equal responsibility. All authors read and approved the final manuscript.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no competing interests.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsJishou UniversityJishouChina
  2. 2.Department of MathematicsSun Yat-sen UniversityGuangzhouChina
  3. 3.School of Mathematics and StatisticsYunnan UniversityKunmingChina

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