Comment on: “Application of the method for the complex KdV equation” [Huiqun Zhang, Commun Nonlinear Sci Numer Simul 15;2010:1700–1704]

Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer

“…These solutions can be found using the simplest equation method [30][31][32][33] for the travelling wave v(ξ, τ ) = y(z), z = ξ − C 0 τ . We look for solution in the form y(z) = a 0 + a 1 w(z) + a 2 w(z) 2 , (5.17) where w(z) is solution of linear ordinary differential equation of the second order [34,35] w zz = A w z + B w + C . (5.18) One of these solution at α 1 < −1 takes the form…”

Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities

“…Once the traveling variable reduction is performed, one cannot avoid to recall that there is a multitude of papers on a variety of effective methods to solve the resulting ODE's based on polynomial ansatze of the solution, in general stemming from the breakthrough tanh-method of Malfliet and Hereman [13][14][15]. We mention the equivalent G ′ /G-expansion method [16], the sinh-cosh [17] and tanh-coth methods [18], the Q-function method [19,20], and the more powerful Jacobi elliptic function method and their extended versions which can be used for more complicated equations such as the double sine-Gordon [21] or to derive doubly periodic wave solutions of a variety of Boussinesq-like equations [18]. In fact, the G ′ /G-expansion method and the tanh method have been already applied to Tzitzéica's equation and its variants in [7,22].…”

Exact Solutions of Equation Generated by the Jaulent-Miodek Hierarchy by(G’/G)-Expansion Method

“…Moreover, Zhang et al have further extended the method to deal with evolution equations with variable coefficients [17]. In fact the ( / )-expansion method has been successfully applied to obtain exact solution for a variety of (NLEEs) [12,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In this paper, the ( / )expansion method is proposed for constructing more general exact solutions of the above nonlinear (2 + 1)-dimensional equation generated by the Jaulent-Miodek Hierarchy.…”