Exact Travelling Wave Solutions Of The Benjamin-bona-mahony-burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/g) Expansion Method

Year 2016, Volume: 4 Issue: 1, 21 - 37, 01.05.2016

O. Gözükızıl T. Aydemir

Abstract

In this paper, we consider some nonlinear pseudoparabolic Benjamin-Bona-Mahony-Burger(BBMB) equations by using the (G′/G) expansion method with the aid of computer algebraic system Maple. These equations are of a class of nonlinear pseudoparabolic or Sobolev-type equations ,α is a fixed positive constant, arising from mathematical physics. The method is straightforward and concise, and it be also applied to other nonlinear pseudoparabolic equations.

Keywords

The (G′/G) expansion method, Travelling wave solution, Nonlinear pseudoparabolic equation, Benjamin-Bona-Mahony-Burger-type(BBMB) equation.

Bu makalede Maple yardımıyla (G′/G) açılım metodu kullanarak lineer olmayan pseudoparabolik

Abstract

Benjamin-Bona-Mahony-Burger(BBMB) denklemlerini ele aldık. Bu denklemler matematiksel fizikte ortaya çıkan, α pozitif bir sabit pozitif bir katsayı olmak üzere

Keywords

The (G′/G) açılım metodu, Yürüyen dalga çözümü, Lineer olmayan pseudoparabolik

References

• [1] M.J.Ablowitz, “H.Segur, Solitons and the inverse scattering transform”, SIAM, Philadelphia, Pa, USA, 1981.
• [2] M.R.Miura, “Backlund transformation”, Springer, Berlin, Germany, 1978.
• [3] C.Rogers, W.F. Shadwick, “Backlund transformations”, Academic Press, New York, NY, USA, 1982.
• [4] V.B.Matveev, M.A.Salle, “Darboux transform and Solitons”, Springer, Berlin, Germany, 1991.
• [5] R.Hirota, “The direct method in soliton theory”, Cambridge University Press, Cambridge, 2004.
• [6] Ş.Akçağıl, Ö.F.Gözükızıl, “The tanh-coth method for some nonlinear pseudoparabolic equations with exact solutions”, Advances in Difference Equations 143, 2013.
• [7] W.Malfiet, “The tanh method: a tool for solving certain classes of nonlinear PDEs, Mathematical Methods in the Applied Sciences” , Vol 28, no.17, pp. 2013-2935, 2005.
• [8] C.T.Yan, “A simple transformation for nonlinear waves”, Physics Letter A 224, 77-84,1996.
• [9] J.H.He, X.H.Wu, “Exp-function method for nonlinear wave equations”, Chaos,Solitons and Fractals, Vol.30, no.3, pp. 700-708, 2006.
• [10] Z.Y.Yan, H.Q.Zhang, “New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water”, Physics Letter A 285, 355-362,2001.
• [11] M.L.Wang, “Exact solutions for a compound KdV-Burgers equation”, Physics Letter A 213, 279- 287,1996.
• [12] F.Tascan, A.Bekir, M.Koparan, “Travelling wave solutions of nonlinear evolution equations by using the first integral method”, Commun. Nonlinear Sci. Numer. Simul. 14 1810-1815, 2009.