Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(6): 060204    DOI: 10.1088/1674-1056/22/6/060204
GENERAL Prev   Next  

Singular solitons and other solutions to a couple of nonlinear wave equations

Mustafa Inca, Esma Ulutaşb, Anjan Biswasc
a Firat University, Department of Mathematics, 23119 Elazğ, Türkiye;
b Bitlis Eren University, Deparment of Statistic, Bitlis, Türkiye;
c Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA
Abstract  This paper addresses the extended (G'/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified Benjamin-Bona-Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, by the aid of ansatz method.
Keywords:  (G'/G)-expansion method      travelling wave solutions      singular soliton      mBBM and Boussinesq equations  
Received:  01 November 2012      Revised:  30 November 2012      Published:  01 May 2013
PACS:  02.30.Jr (Partial differential equations)  
  02.60.Cb (Numerical simulation; solution of equations)  
Corresponding Authors:  Mustafa Inc     E-mail:  minc@firat.edu.tr

Cite this article: 

Mustafa Inc, Esma Ulutaş, Anjan Biswas Singular solitons and other solutions to a couple of nonlinear wave equations 2013 Chin. Phys. B 22 060204

[1] Debtnath L 1997 Nonlinear Partial Differential Equations for Scientists and Engineers (Boston: Birkhauser) pp. 424-431
[2] Wazwaz A M 2002 Partial Differential Equations: Methods and Applications (Rotterdam: Balkema) pp. 387-392
[3] Ablowitz M J and Clarkson P A 1991 Solitons, Non-linear Equations and Inverse Scattering Transform (Cambridge: Cambridge University Press) p. 70
[4] Wang M L 1995 Phys. Lett. A 199 169
[5] Wang M L 1996 Phys. Lett. A 213 279
[6] Wang M L, Zhou Y B and Li Z B 1996 Phys. Lett. A 216 67
[7] Yan Z Y and Zhang H Q 2001 Phys. Lett. A 285 355
[8] Hirota R 1973 J. Math. Phys. 14 810
[9] Hirota R and Satsuma J 1981 Phys. Lett. A 85 407
[10] Satsuma J and Hirota R 1982 J. Phys. Soc. Jpn. 51 3390
[11] Yan C T 1996 Phys. Lett. A 224 77
[12] Yan Z Y and Zhang H Q 2000 Appl. Math. Mech. 22 541
[13] Abourabia A M and El Horbaty M M 2006 Chaos, Solitons and Fractals 29 354
[14] Liu J B and Yang K Q 2004 Chaos, Solitons and Fractals 22 111
[15] Zhang S 2006 Phys. Lett. A 358 414
[16] Zhang S 2006 Chaos, Solitons and Fractals 30 1213
[17] Zhang S 2007 Chaos, Solitons and Fractals 32 847
[18] Zhang S 2007 Chaos, Solitons and Fractals 32 1375
[19] Zhang S and Xia T C 2006 Appl. Math. Comput. 183 1190
[20] Zhang S 2007 Appl. Math. Comput. 189 836
[21] Abdou M A 2007 Chaos, Solitons and Fractals 31 95
[22] Sirendaoreji and Song J 2003 Phys. Lett. A 309 387
[23] Zhang S 2007 Phys. Lett. A 368 470
[24] Zhang S and Xia T C 2007 Phys. Lett. A 363 356
[25] Zhang S and Xia T C 2007 J. Phys. A: Math. Theor. 40 227
[26] Zhang S 2007 Appl. Math. Comput. 188 1
[27] Zhang S 2007 Comput. Math. Appl. 54 1028
[28] Shehata A R 2010 Appl. Math. Comput. 217 1
[29] Aslan İ 2010 Appl. Math. Comput. 216 2778
[30] Zuo J M 2010 Appl. Math. Comput. 217 376
[31] Ö zis T and Aslan İ 2010 Appl. Math. Comput. 216 2360
[32] Biswas A and Konar S 2008 Commun. Nonlinear Sci. Numer. Simul. 13 703
[33] Biswas A, Milovic D and Ranasinghe A 2009 Commun. Nonlinear Sci. Numer. Simul. 14 3738
[34] Ebadi G, Johnson S, Zerad E and Biswas A 2012 J. King Saud University Sci. 24 237
[35] Krishnan E V, Kumar S and Biswas A 2012 Nonlinear Dyn. 70 1213
[36] Yusufoğlu E and Bekir A 2008 Chaos, Solitons and Fractals 38 1126
[37] Wazwaz A 2008 Commun. Nonlinear Sci. Numer. Simul. 13 889
[38] Wang M L, Li X Z and Zhang J L 2008 Phys. Lett. A 372 417
[1] Applications of the first integral method to nonlinear evolution equations
Filiz Ta, scan, Ahmet Bekir. Chin. Phys. B, 2010, 19(8): 080201.
[2] Travelling solitary wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order
Deng Xi-Jun, Yan Zi-Zong, Han Li-Bo. Chin. Phys. B, 2009, 18(8): 3169-3173.
[3] A new variable coefficient algebraic method and non-travelling wave solutions of nonlinear equations
Lu Bin, Zhang Hong-Qing. Chin. Phys. B, 2008, 17(11): 3974-3984.
[4] Hyperbolic function method for solving nonlinear differential-different equations
Zhu Jia-Min. Chin. Phys. B, 2005, 14(7): 1290-1295.
No Suggested Reading articles found!