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

doi:10.1088/1674-1056/20/1/010205

中国物理B ›› 2011, Vol. 20 ›› Issue (1): 10205-010205.doi: 10.1088/1674-1056/20/1/010205

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

左进明, 张耀明

School of Science, Shandong University of Technology, Zibo 255049, China

收稿日期:2010-06-14 修回日期:2010-07-16 出版日期:2011-01-15 发布日期:2011-01-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10871117 and 10571110).

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

Received:2010-06-14 Revised:2010-07-16 Online:2011-01-15 Published:2011-01-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10871117 and 10571110).

摘要/Abstract

摘要： 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.

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.

Key words: coupled Burgers equation, high-order Boussinesq–Burgers equation, Hirota's bilinear method

中图分类号: (Integrable systems)

02.30.Ik

02.30.Jr (Partial differential equations) 04.20.Jb (Exact solutions)

左进明, 张耀明. The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq–Burgers equation[J]. 中国物理B, 2011, 20(1): 10205-010205.

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[J]. Chin. Phys. B, 2011, 20(1): 10205-010205.

参考文献 22

[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

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

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

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