Lump and interaction solutions to the (3+1)-dimensional Burgers equation

doi:10.1088/1674-1056/ab6964

中国物理B ›› 2020, Vol. 29 ›› Issue (3): 30201-030201.doi: 10.1088/1674-1056/ab6964

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 下一篇

Lump and interaction solutions to the (3+1)-dimensional Burgers equation

Jian Liu(刘健), Jian-Wen Wu(吴剑文)

1 Department of Mathematics and Physics, Quzhou University, Quzhou 324000, China;
2 Department of Physics, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2019-11-06 修回日期:2019-12-27 出版日期:2020-03-05 发布日期:2020-03-05
通讯作者: Jian Liu E-mail:jian.liu_math@qzc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11501323, 11701323, and 11605102).

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

Received:2019-11-06 Revised:2019-12-27 Online:2020-03-05 Published:2020-03-05
Contact: Jian Liu E-mail:jian.liu_math@qzc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11501323, 11701323, and 11605102).

摘要/Abstract

摘要： 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.

关键词: (3+1)-dimensional Burgers equation, lump solution, interaction wave solution, bilinear form

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.

Key words: (3+1)-dimensional Burgers equation, lump solution, interaction wave solution, bilinear form

中图分类号: (Partial differential equations)

02.30.Jr

02.70.Wz (Symbolic computation (computer algebra)) 02.60.Cb (Numerical simulation; solution of equations)

刘健, 吴剑文. Lump and interaction solutions to the (3+1)-dimensional Burgers equation[J]. 中国物理B, 2020, 29(3): 30201-030201.

Jian Liu(刘健), Jian-Wen Wu(吴剑文). Lump and interaction solutions to the (3+1)-dimensional Burgers equation[J]. Chin. Phys. B, 2020, 29(3): 30201-030201.

参考文献 28

[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 doi: 10.1016/0375-9601(77)90875-1
[3]	Leblond H and Manna M 2007 Phys. Rev. Lett. 99 064102 doi: 10.1103/PhysRevLett.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 doi: 10.1103/PhysRevLett.89.204501
[6]	Ma W X 2015 Phys. Lett. A 379 1975 doi: 10.1016/j.physleta.2015.06.061
[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 doi: 10.1007/s11071-019-04850-9
[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 doi: 10.1016/j.wavemoti.2017.10.012
[12]	Hao X Z, Liu Y P, Li Z B and Ma W X 2019 Comput. Math. Appl. 77 724 doi: 10.1016/j.camwa.2018.10.007
[13]	Yang Y Q, Yan Z Y and Malomed B A 2015 Chaos 25 103112 doi: 10.1063/1.4931594
[14]	Wang X B, Tian S F, Qin C Y and Zhang T T 2017 Appl. Math. Lett. 68 40 doi: 10.1016/j.aml.2016.12.009
[15]	Ren B, Ma W X and Yu J 2019 Nonlinear Dyn. 96 717 doi: 10.1007/s11071-019-04816-x
[16]	Tang Y N, Tao S Q, Zhou M L and Guan Q 2017 Nonlinear Dyn. 89 429 doi: 10.1007/s11071-017-3462-9
[17]	Liu J G and He Y 2018 Nonlinear Dyn. 92 1103 doi: 10.1007/s11071-018-4111-7
[18]	Ma W X, Yong X L and Zhang H Q 2018 Comput. Math. Appl. 75 289 doi: 10.1016/j.camwa.2017.09.013
[19]	Lou S Y and Lin J 2018 Chin. Phys. Lett. 35 050202 doi: 10.1088/0256-307X/35/5/050202
[20]	Kofane T C, Fokou M, Mohamadou A and Yomba E 2017 Eur. Phys. J. Plus 132 465 doi: 10.1140/epjp/i2017-11747-6
[21]	An H L, Feng D and Zhu H X 2019 Nonlinear Dyn. 98 1275 doi: 10.1007/s11071-019-05261-6
[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 doi: 10.1016/j.physleta.2008.11.018
[24]	Yin J P and Lou S Y 2003 Chin. Phys. Lett. 20 1448 doi: 10.1088/0256-307X/20/9/311
[25]	Dai C Q and Yu F B 2014 Wave Motion 51 52 doi: 10.1016/j.wavemoti.2013.06.002
[26]	Tang X Y and Lou S Y 2003 Chin. Phys. Lett. 20 335 doi: 10.1088/0256-307X/20/3/306
[27]	Wang H 2018 Appl. Math. Lett. 85 27 doi: 10.1016/j.aml.2018.05.010
[28]	Wang S, Tang X Y and Lou S Y 2004 Chaos Solitons Fract. 21 231 doi: 10.1016/j.chaos.2003.10.014

Lump and interaction solutions to the (3+1)-dimensional Burgers equation

Lump and interaction solutions to the (3+1)-dimensional Burgers equation

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 28

相关文章 7

Metrics

本文评价

推荐阅读 0

[1]	Ping Liu(刘萍), Bing Huang(黄兵), Bo Ren(任博), and Jian-Rong Yang(杨建荣). Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves[J]. 中国物理B, 2021, 30(8): 80203-080203.
[2]	王海峰, 张玉峰. Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation[J]. 中国物理B, 2020, 29(4): 40501-040501.
[3]	Abdselam Silem, 张成, 张大军. Dynamics of three nonisospectral nonlinear Schrödinger equations[J]. 中国物理B, 2019, 28(2): 20202-020202.
[4]	程雪苹, 马文秀, 杨云青. Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions[J]. 中国物理B, 2019, 28(10): 100203-100203.
[5]	郑攀峰, 贾曼. A more general form of lump solution, lumpoff, and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation[J]. 中国物理B, 2018, 27(12): 120201-120201.
[6]	张雯婷, 戴朝卿, 陈未路. Interactions among special embed-solitons for the (3+1)-dimensional Burgers equation[J]. Chin. Phys. B, 2013, 22(4): 40509-040509.
[7]	唐亚宁, 马文秀, 徐伟. Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation[J]. 中国物理B, 2012, 21(7): 70212-070212.