A modified tanh–coth method for solving the KdV and the KdV–Burgers’ equations

Application of the exp-function method for solving nonlinear reaction–diffusion equations arising in mathematical biology

“…He analyzed the paper of Wazzan [21] and demonstrated that all of his solutions were not new and could be transformed to known solutions.…”

New Exact Solutions of Some Nonlinear Evolution Equations by Sub-Ode Method

“…Certainly there are many different exact solutions of Eq.(10). This equation has soliton, rational and elliptic solutions [2,15]. Recently Wang [2] made an effort to obtain some new exact solutions of the Korteweg-de Vries equation.…”

“…By substituting (15) and (16) into Eq. (11) and collecting all terms with the same power of F G together, the left-hand side of Eq.…”

Exact traveling wave solutions for some nonlinear evolution equations

“…The concept of tanh-function method was first proposed in [15] and it was used to obtain the exact traveling wave solutions to many nonlinear problems. A search in the literature have revealed that the various types of tanh-function methods have been proposed and applied to many nonlinear partial differential equations [8,13,19,10,11]. The generalized tanh-function method is used for constructing exact traveling wave solutions of general Burgers-Fisher and the Kuramoto-Sivashinsky equations [8].…”

“…More recently, ElWakil et al [11] proposed a modified tanh-coth method for constructing soliton and periodic solutions of nonlinear equations. Wazzan [19] applied the modified tanhcoth method for obtaining new traveling wave solutions of KdV and the KdV-Burgers equations. The main idea of this method is that it uses the Riccati equation and its solutions.…”