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

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Abstract

The general form of Benjamin-Bona-Mahony equation (BBM) is

$u_t + au_x + bu_{xxt} + (g(u))_x = 0,a,b \in \mathbb{R},$

where ab ≠ 0 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 ≠ 0, and qp ≠ 0, 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.

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

    Reza Abazari

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  1. Reza Abazari
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Abazari, R. On the exact solitary wave solutions of a special class of Benjamin-Bona-Mahony equation. Comput. Math. and Math. Phys. 53, 1371–1376 (2013). https://doi.org/10.1134/S0965542513090133

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  • DOI: https://doi.org/10.1134/S0965542513090133

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