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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

[1] Dauxois T and Peyrard M 2006 Physics of Solitons (Cambridge: Cambridge Univ. Press)
[2] Manakov S V, Zakhorov V E and Bordag L A 1977 Phys. Lett. 63 205
[3] Leblond H and Manna M 2007 Phys. Rev. Lett. 99 064102
[4] Bergshoeff E and Townsend P K 1999 J. High Energy Phys. 9905 021
[5] Falcon E, Laroche C and Fauve S 2002 Phys. Rev. Lett. 89 204501
[6] Ma W X 2015 Phys. Lett. A 379 1975
[7] Ma W X and Zhou Y 2017 J. Differential Equations 264 2633
[8] Zhang H Q and Ma W X 2018 Nonlinear Dyn.87 2305
[9] Guo F and Lin J 2019 Nonlinear Dyn. 96 1233
[10] Ren B, Ma W X and Yu J 2019 Comput. Math. Appl.77 2086
[11] Yang Y Q, Wang X and Cheng X P 2018 Wave Motion 77 1
[12] Hao X Z, Liu Y P, Li Z B and Ma W X 2019 Comput. Math. Appl. 77 724
[13] Yang Y Q, Yan Z Y and Malomed B A 2015 Chaos 25 103112
[14] Wang X B, Tian S F, Qin C Y and Zhang T T 2017 Appl. Math. Lett. 68 40
[15] Ren B, Ma W X and Yu J 2019 Nonlinear Dyn. 96 717
[16] Tang Y N, Tao S Q, Zhou M L and Guan Q 2017 Nonlinear Dyn. 89 429
[17] Liu J G and He Y 2018 Nonlinear Dyn. 92 1103
[18] Ma W X, Yong X L and Zhang H Q 2018 Comput. Math. Appl. 75 289
[19] Lou S Y and Lin J 2018 Chin. Phys. Lett. 35 050202
[20] Kofane T C, Fokou M, Mohamadou A and Yomba E 2017 Eur. Phys. J. Plus 132 465
[21] An H L, Feng D and Zhu H X 2019 Nonlinear Dyn. 98 1275
[22] Li W T, Zhang Z, Yang X Y and Li B 2019 Int. J. Mod. Phys. B 22 1950255
[23] Dai C Q and Wang Y Y 2009 Phys. Lett. A 373 181
[24] Yin J P and Lou S Y 2003 Chin. Phys. Lett. 20 1448
[25] Dai C Q and Yu F B 2014 Wave Motion 51 52
[26] Tang X Y and Lou S Y 2003 Chin. Phys. Lett. 20 335
[27] Wang H 2018 Appl. Math. Lett. 85 27
[28] Wang S, Tang X Y and Lou S Y 2004 Chaos Solitons Fract. 21 231
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