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In this letter, we establish some exact solutions for complex nonlinear Klein–Gordon equation u tt − p 2 u xx + qu + r | u | 2 u = 0 , where pqr ≠ 0 . The ( G ′/ G )-expansion method is used to construct exact periodic and soliton solutions of this equation. Our work is motivated by the fact that the ( G ′/ G )-expansion method provides not only more general forms of solutions but also periodic and solitary waves. As a result, hyperbolic function solutions, trigonometric function solutions and rational function solutions with parameters are obtained and shown in some figures. These solutions may be important for the explanation of some practical physical and engineering problems. [ABSTRACT FROM AUTHOR]

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 C2-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. [ABSTRACT FROM AUTHOR]

This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011) and (Kılıcman and Abazari, 2012), that focuses on the application of (G'/G)-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientist Joseph Valentin Boussinesq (1842-1929) described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation. [ABSTRACT FROM AUTHOR]

We establish exact solutions for the Schrödinger-Boussinesq System iut + uxx - auv = 0, vtt - vxx + vxxxx - b(|u|2)xx = 0, where a and b are real constants. The (G'/G)-expansion method is used to construct exact periodic and soliton solutions of this equation. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. As a result, hyperbolic function solutions and trigonometric function solutions with parameters are obtained. These solutions may be important and of significance for the explanation of some practical physical problems. [ABSTRACT FROM AUTHOR]

The (G'/G)-expansion method is proposed to construct the exact traveling solutions to Hirota-Ramani equation: ut - uxxt + aut (1 - ut) = 0, where a ≠ 0. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system. [ABSTRACT FROM AUTHOR]

Abstract: In this work, the -expansion method is applied for constructing more general exact solutions of the three nonlinear evolution equations with physical interest namely, the Tzitzéica equation, the Dodd–Bullough–Mikhailov (DBM) equation and the Tzitzéica–Dodd–Bullough (TDB) equation. Our work is motivated by the fact that the -expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system. [Copyright &y& Elsevier]