Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(1): 010205    DOI: 10.1088/1674-1056/20/1/010205
GENERAL Prev   Next  

The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq–Burgers equation

Zuo Jin-Ming(左进明) and Zhang Yao-Ming(张耀明)
School of Science, Shandong University of Technology, Zibo 255049, China
Abstract  This paper studies the coupled Burgers equation and the high-order Boussinesq–Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink (soliton) solutions and multiple-singular-kink (soliton) solutions are derived for the two equations.
Keywords:  coupled Burgers equation      high-order Boussinesq–Burgers equation      Hirota's bilinear method  
Received:  14 June 2010      Revised:  16 July 2010      Accepted manuscript online: 
PACS:  02.30.Ik (Integrable systems)  
  02.30.Jr (Partial differential equations)  
  04.20.Jb (Exact solutions)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10871117 and 10571110).

Cite this article: 

Zuo Jin-Ming(左进明) and Zhang Yao-Ming(张耀明) The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq–Burgers equation 2011 Chin. Phys. B 20 010205

[1] Hirota R 1974 wxProg. Theor. Phys.52 1498
[2] Hirota R 2004 wxThe Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
[3] Hirota R 1971 wxPhys. Rev. Lett.27 1192
[4] Hirota R 1972 wxJ. Phys. Soc. Jpn.33 1456
[5] Hirota R 1972 wxJ. Phys. Soc. Jpn.33 1459
[6] Sawada K and Kotera T 1974 wxProg. Theor. Phys.51 1355
[7] Kadomtsev B B and Petviashvili V I 1970 wxSov. Phys. Dokl.15 539
[8] Hirota R and Ito M 1983 wxJ. Phys. Soc. Jpn.52 744
[9] Zhang J F and Guo G P 2003 wxActa Phys. Sin.52 2359 (in Chinese)
[10] Zhaqilao and Li Z B 2008 wxChin. Phys. B17 2333
[11] Wazwaz A M 2009 wxAppl. Math. Comput.211 495
[12] Wu J P 2010 wxCommun. Theor. Phys.53 812
[13] Yao Y Q, Chen D Y and Zeng Y B 2010 wxNonlinear Anal.72 57
[14] Wazwaz A M 2010 wxNonlinear Anal.72 1314
[15] Wang M L, Zhou Y B and Li Z B 1996 wxPhys. Lett. A216 67
[16] Fan E G and Zhang H Q 1998 wxActa Phys. Sin.47 353 (in Chinese)
[17] He J H and Wu X H 2006 wxChaos, Solitons and Fractals30 700
[18] Yang H J, Shi Y R, Duan W S and L"u K P 2007 wxActa Phys. Sin.56 3064 (in Chinese)
[19] Wang M L, Li X Z and Zhang J L 2008 wxPhys. Lett. A372 417
[20] Zuo J M 2009 wxAppl. Math. Comput.215 835
[21] Li W A, Chen H and Zhang G C 2009 wxChin. Phys. B18 400
[22] Deng X J, Yan Z Z and Han L B 2009 wxChin. Phys. B18 3169
[1] Local discontinuous Galerkin method for solving Burgers and coupled Burgers equations
Zhang Rong-Pei(张荣培), Yu Xi-Jun(蔚喜军), and Zhao Guo-Zhong(赵国忠) . Chin. Phys. B, 2011, 20(11): 110205.
[2] New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems
Chen Jin-Bing(陈金兵), Geng Xian-Guo(耿献国), and Qiao Zhi-Jun(乔志军). Chin. Phys. B, 2010, 19(9): 090403.
No Suggested Reading articles found!