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

doi:10.1088/1674-1056/22/6/060204

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60204-060204.doi: 10.1088/1674-1056/22/6/060204

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

Mustafa Inc^a, Esma Ulutaş^b, Anjan Biswas^c

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

收稿日期:2012-11-01 修回日期:2012-11-30 出版日期:2013-05-01 发布日期:2013-05-01

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

Mustafa Inc^a, Esma Ulutaş^b, Anjan Biswas^c

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

Received:2012-11-01 Revised:2012-11-30 Online:2013-05-01 Published:2013-05-01
Contact: Mustafa Inc E-mail:minc@firat.edu.tr

摘要/Abstract

摘要： 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.

关键词: (G'/G)-expansion method, travelling wave solutions, singular soliton, mBBM and Boussinesq equations

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.

Key words: (G'/G)-expansion method, travelling wave solutions, singular soliton, mBBM and Boussinesq equations

中图分类号: (Partial differential equations)

02.30.Jr

02.60.Cb (Numerical simulation; solution of equations)

Mustafa Inc, Esma Ulutaş, Anjan Biswas. Singular solitons and other solutions to a couple of nonlinear wave equations[J]. 中国物理B, 2013, 22(6): 60204-060204.

Mustafa Inc, Esma Ulutaş, Anjan Biswas. Singular solitons and other solutions to a couple of nonlinear wave equations[J]. Chin. Phys. B, 2013, 22(6): 60204-060204.

参考文献 38

[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

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

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

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