Abstract
This paper proposes a new approach of $\left(\acute{G}/G\right)$ -expansion method for constructing more general exact solutions of nonlinear evolution equation. By using this method numerous new and more general exact solutions have been obtained. We will apply this new method to solve the nonlinear KdV equation. Various exact traveling wave solutions of these equations are obtained that include the exponential function solutions, the hyperbolic function solutions and the trigonometric function solutions. Further, the method is efficient to solve nonlinear evolution equations in many areas such as physics and engineering.
Highlights
Several phenomena in various fields are frequently described by nonlinear partial differential equation (NLPDEs), for instance nonlinear optics, elastic media, plasma physics, fluid mechanics, chemistry, biology and many others (Rogers & Shadwick, 1982; Akbar, Ali, & Zayed, 2012)
This paper proposes a new approach of G/G -expansion method for constructing more general exact solutions of nonlinear evolution equation
Several phenomena in various fields are frequently described by nonlinear partial differential equation (NLPDEs), for instance nonlinear optics, elastic media, plasma physics, fluid mechanics, chemistry, biology and many others (Rogers & Shadwick, 1982; Akbar, Ali, & Zayed, 2012)
Summary
Several phenomena in various fields are frequently described by nonlinear partial differential equation (NLPDEs), for instance nonlinear optics, elastic media, plasma physics, fluid mechanics, chemistry, biology and many others (Rogers & Shadwick, 1982; Akbar, Ali, & Zayed, 2012). D. Liu, & Zhao, 2001), the generalized Riccati equation method (Yan & Zhang, 2001; Naher & Abdullah, 2012), the tanh-coth method (Malfliet, 1992; Wazwaz, 2007), the F-expansion method (Wang & Li, 2005; Abdou, 2007), the variational iteration method Step 1 Use the transformation u (x, t) = u (ξ); ξ = k1 x + k2t, where k1, k2 are constant, to be determined latter. Step 3 Find the value of m by balancing the highest order derivative and nonlinear terms in (3). G G of the obtained systems numerator to zero, produces a set of over determined nonlinear algebraic equations for k1, k2, A1, A2, B1, B2 and αi (i = 0, 1, 2, ...m).
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