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

Yıl 2016, Cilt: 4 Sayı: 1, 21 - 37, 01.05.2016

Öz

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.

Kaynakça

  • [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.

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

Yıl 2016, Cilt: 4 Sayı: 1, 21 - 37, 01.05.2016

Öz

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

Kaynakça

  • [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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA22PG45ZE
Bölüm Araştırma Makalesi
Yazarlar

O. Gözükızıl Bu kişi benim

T. Aydemir

Yayımlanma Tarihi 1 Mayıs 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 1

Kaynak Göster

APA Gözükızıl, O., & Aydemir, T. (2016). Exact Travelling Wave Solutions Of The Benjamin-bona-mahony-burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/g) Expansion Method. MANAS Journal of Engineering, 4(1), 21-37.
AMA Gözükızıl O, Aydemir T. Exact Travelling Wave Solutions Of The Benjamin-bona-mahony-burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/g) Expansion Method. MJEN. Mayıs 2016;4(1):21-37.
Chicago Gözükızıl, O., ve T. Aydemir. “Exact Travelling Wave Solutions Of The Benjamin-Bona-Mahony-Burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/G) Expansion Method”. MANAS Journal of Engineering 4, sy. 1 (Mayıs 2016): 21-37.
EndNote Gözükızıl O, Aydemir T (01 Mayıs 2016) Exact Travelling Wave Solutions Of The Benjamin-bona-mahony-burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/g) Expansion Method. MANAS Journal of Engineering 4 1 21–37.
IEEE O. Gözükızıl ve T. Aydemir, “Exact Travelling Wave Solutions Of The Benjamin-bona-mahony-burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/g) Expansion Method”, MJEN, c. 4, sy. 1, ss. 21–37, 2016.
ISNAD Gözükızıl, O. - Aydemir, T. “Exact Travelling Wave Solutions Of The Benjamin-Bona-Mahony-Burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/G) Expansion Method”. MANAS Journal of Engineering 4/1 (Mayıs 2016), 21-37.
JAMA Gözükızıl O, Aydemir T. Exact Travelling Wave Solutions Of The Benjamin-bona-mahony-burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/g) Expansion Method. MJEN. 2016;4:21–37.
MLA Gözükızıl, O. ve T. Aydemir. “Exact Travelling Wave Solutions Of The Benjamin-Bona-Mahony-Burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/G) Expansion Method”. MANAS Journal of Engineering, c. 4, sy. 1, 2016, ss. 21-37.
Vancouver Gözükızıl O, Aydemir T. Exact Travelling Wave Solutions Of The Benjamin-bona-mahony-burgers Type (bbmb) Nonlinear Pseudoparabolic Equations By Using The (g’/g) Expansion Method. MJEN. 2016;4(1):21-37.

Manas Journal of Engineering 

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