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Chin. Phys. B, 2014, Vol. 23(2): 020203    DOI: 10.1088/1674-1056/23/2/020203
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A novel (G’/G)-expansion method and its application to the Boussinesq equation

Md. Nur Alama, Md. Ali Akbarb, Syed Tauseef Mohyud-Dinc
a Department of Mathematics, Pabna University of Science and Technology, Bangladesh;
b Department of Applied Mathematics, University of Rajshahi, Bangladesh;
c Department of Mathematics, HITEC University, Taxila Cantt, Pakistan
Abstract  In this article, a novel (G’/G)-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new (G’/G)-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.
Keywords:  (G’/G)-expansion method      Boussinesq equation      solitary wave solutions      auxiliary nonlinear ordinary differential equation  
Received:  26 April 2013      Revised:  28 June 2013      Published:  12 December 2013
PACS:  02.30.Jr (Partial differential equations)  
  02.30.Ik (Integrable systems)  
  04.20.Jb (Exact solutions)  
  05.45.Yv (Solitons)  
Corresponding Authors:  Syed Tauseef Mohyud-Din     E-mail:  syedtauseefs@hotmail.com
About author:  02.30.Jr; 02.30.Ik; 04.20.Jb; 05.45.Yv

Cite this article: 

Md. Nur Alam, Md. Ali Akbar, Syed Tauseef Mohyud-Din A novel (G’/G)-expansion method and its application to the Boussinesq equation 2014 Chin. Phys. B 23 020203

[1] Russell J S 1844 Report on Waves (Report of the Fourteenth Meeting of the British Association for the Advancement of Science (New York, September 1844) p. 311
[2] Ablowitz M J and Clarkson P A 1991 Soliton, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
[3] Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
[4] Matveev V B and Salle M A 1991 Darboux Transformation and Solitons (Berlin: Springer)
[5] Bai C L 2004 Chin. Phys. 13 1
[6] Malfliet W and Hereman W 1996 Phys. Scr. 54 569
[7] Pan J T and Gong L X 2007 Acta Phys. Sin. 56 5585 (in Chinese)
[8] Bluman G W and Kumei S 1989 Symmetries and Differential Equations (Berlin: Springer)
[9] Weiss J, Tabor M and Carnevale G 1983 J. Math. Phys. 24 522
[10] Akbar M A and Ali N H M 2012 World Appl. Sci. J. 17 1603
[11] Naher H, Abdullah A F and Akbar M A 2012 J. Appl. Math. Article ID 575387 14 pages. doi: 10.1155/2012/575387
[12] Wazwaz A M 2002 Partial Differential Equations: Method and Applications (Taylor and Francis)
[13] Wang M 1995 Phys. Lett. A 199 169
[14] Wang M, Li X and Zhang J 2008 Phys. Lett. A 372 417
[15] Akbar M A, Ali N H M and Zayed E M E 2013 Commun. Theor. Phys. 57 173
[16] Akbar M A, Ali N H M and Zayed E M E 2012 Math. Prob. Engr. Article ID 459879 22 pages. doi: 10.1155/2012/459879
[17] Akbar M A, Ali N H M and Mohyud-Din S T 2012 Int. J. Phys. Sci. 7 743
[18] Akbar M A, Ali N H M and Mohyud-Din S T 2012 World Appl. Sci. J. 16 1551
[19] Zayed E M E 2009 J. Appl. Math. Comput. 30 89
[20] Zhang J, Wei X and Lu Y 2008 Phys. Lett. A 372 3653
[21] Zhang J, Jiang F and Zhao X 2010 Int. J. Comput. Math. 87 1716
[22] Zayed E M E 2009 J. Phys. A: Math. Theor. 42 195202
[23] Zayed E M E 2011 J. Appl. Math. & Informatics 29 351
[24] Neyrame A, Roozi A, Hosseini S S and Shafiof S M 2012 J. King Saud Univ. (Sci.) 22 275
[25] Zhu S 2008 Chaos, Solitons and Fractals 37 1335
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