The tanh and the sine–cosine methods for a reliable treatment of the modified equal width equation and its variants

Exact traveling wave solutions of some nonlinear evolution equations

“…The medium equal width (MEW) equation is used as a model PDE for the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes [24] and is given by …”

The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method

“…Exact solutions of the KdV equation with a variable nonlinear term coefficient have been developed through a variety of analytical techniques, such as tanh-coth method [5][6][7], sine-cosine method [5], Hirota's direct method [3,[8][9], and Exp-function method [10], among others [11][12][13].…”

“…From the literature [3,5,[7][8][9][10], it can be found that all exact solutions of the KdV equation will approach to infinity and do not satisfy the continuity condition when the nonlinear term coefficient is zero. Obviously, they can not be reducible to linear solutions.…”

“…Several numerical results are illustrated, through which a new phenomenon is revealed. [5][6][7], the sine-cosine method [5], the Exp-function method [10] and others [11][12][13] where c is the wave speed. It is noted that equations (2.1-8) can all be obtained by the tanh-coth method [3], while equations (2.1-2) and (2.5) can also be found by the sine-cosine method [3].…”

Application of G'/G expansion method to two concert problems

“…The nonlinear equations of mathematical physics are major subjects in physics and engineering, and various powerful methods have been presented, such as the tanh method [1][2], sine-cosine method [3], homotopy perturbation method [4][5], variational iteration method [6][7], Adomian decomposition method [8], Exp-function method [9][10][11], and many others [12][13]. Very recently, Wang et al [14] introduced a new method called the G G  expansion method to look for travelling wave solutions of nonlinear evolution equations.…”