Abstract
This paper elucidates the main advantages of the exp-function method in finding exact solutions of nonlinear wave equations. By the aid of some mathematical software, the solution process becomes extremely simple and accessible.
Highlights
One of the most important aspects in nonlinear science is how to solve an exact solution of a nonlinear equation
According to the exp-function method [15,16,17], we introduce a complex variation ξ defined as ξ = kx + ωt
Balancing highest order of exp-function in (9), we have 3c + p = c + 3p, which leads to the result p = c
Summary
One of the most important aspects in nonlinear science is how to solve an exact solution of a nonlinear equation. Many different methods have appeared, among which the homotopy perturbation method [1,2,3,4], the tanhmethod [5], the sinh-method [6, 7], and the F-expansion method [8,9,10,11] have caught much attention; all these methods are valid for some special kinds of nonlinear equations. It is very much needed to find a universal approach to nonlinear equations; this is very challenging and the exp-function method [12,13,14,15] meets this requirement. The exp-function method itself is mathematically beautiful and extremely accessible to nonmathematicians. The use of the method requires no special knowledge of advanced calculus, and it is especially effective for solitary solutions
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