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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 9, Page 1554 (Mi zvmmf9920)  

This article is cited in 2 scientific papers (total in 2 papers)

On the exact solitary wave solutions of a special class of Benjamin–Bona–Mahony equation

Reza Abazari

Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran

Abstract: The general form of Benjamin-Bona-Mahony equation (BBM) is $ u_t+au_x+bu_{xxt}+(g(u))_x=0,\quad a,b\in\mathbb{R}$, where $ab\ne0$ and $g(u)$ is a $C^2$-smooth nonlinear function, has been proposed by Benjamin et al. In [1] and describes approximately the unidirectional propagation of long wave in certain nonlinear dispersive systems. In this payer, we consider a new class of Benjamin–Bona–Mahony equation (BBM) $u_t+au_x+bu_{xxt}+(pe^u+qe^{-u})_x=0$, $a, b, p, q \in\mathbb{R}$, where $ab\ne0$, and $qp\ne0$, and we obtain new exact solutions for it by using the well-known $(G'/G)$-expansion method. New periodic and solitary wave solutions for these nonlinear equation are formally derived.

Key words: generalized Benjamin-Bona-Mahony (gBBM) equation, solitary wave solutions; $(G'/G)$-expansion method, hyperbolic function solutions, trigonometric function solutions.

DOI: https://doi.org/10.7868/S0044466913090123

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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:9, 1371–1376

Bibliographic databases:

Document Type: Article
UDC: 519.634
MSC: 35Q51, 35Q53, 37K10
Received: 15.03.2013
Revised: 01.04.2013
Language: English

Citation: Reza Abazari, “On the exact solitary wave solutions of a special class of Benjamin–Bona–Mahony equation”, Zh. Vychisl. Mat. Mat. Fiz., 53:9 (2013), 1554; Comput. Math. Math. Phys., 53:9 (2013), 1371–1376

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. Abazari, Sh. Jamshidzadeh, A. Biswas, “Solitary wave solutions of coupled boussinesq equation”, Complexity, 21:S2 (2016), 151–155  crossref  mathscinet  isi  scopus
    2. Sirendaoreji, “Unified Riccati equation expansion method and its application to two new classes of Benjamin-Bona-Mahony equations”, Nonlinear Dyn., 89:1 (2017), 333–344  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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