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 Chin. Phys. B, 2020, Vol. 29(3): 030201    DOI: 10.1088/1674-1056/ab6964
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# Lump and interaction solutions to the (3+1)-dimensional Burgers equation

Jian Liu(刘健)1, Jian-Wen Wu(吴剑文)2
1 Department of Mathematics and Physics, Quzhou University, Quzhou 324000, China;
2 Department of Physics, Zhejiang Normal University, Jinhua 321004, China
Abstract  The (3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics, is considered. Two types of semi-rational solutions, namely, the lump-kink solution and the lump-two kinks solution, are constructed from the quadratic function ansatz. Some interesting features of interactions between lumps and other solitons are revealed analytically and shown graphically, such as fusion and fission processes.
Keywords:  (3+1)-dimensional Burgers equation      lump solution      interaction wave solution      bilinear form
Received:  06 November 2019      Revised:  27 December 2019      Published:  05 March 2020
 PACS: 02.30.Jr (Partial differential equations) 02.70.Wz (Symbolic computation (computer algebra)) 02.60.Cb (Numerical simulation; solution of equations)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11501323, 11701323, and 11605102).
Corresponding Authors:  Jian Liu     E-mail:  jian.liu_math@qzc.edu.cn

#### Cite this article:

Jian Liu(刘健), Jian-Wen Wu(吴剑文) Lump and interaction solutions to the (3+1)-dimensional Burgers equation 2020 Chin. Phys. B 29 030201

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