New exact solutions to the KdV–Burgers–Kuramoto equation

Method of the Logistic Function for Finding Analytical Solutions of Nonlinear Differential Equations

“…(8) and its generalizations were considered many times. For example, the exact solutions of these equations were obtained and re-discovered in works [6,7,[38][39][40][41][42][43][44][45][46].…”

Classical and nonclassical symmetries for a Kuramoto–Sivashinsky equation with dispersive effects

“…The Kuramoto-Sivashinsky (KS) equation has been studied by many authors [1][2][3]. There have been several generalizations of the KS equation such as the generalized KS (GKS) with dispersive effects:…”

“…In order to obtain analytical solutions, several methods have been applied for some particular cases of (1). In this sense, for f (u) = u 2 /2, constant and g = 0, Equation (1) is KS equation, and in [1] exact travelling wave solutions are obtained using trigonometric functions expansions method.…”

“…In order to obtain analytical solutions, several methods have been applied for some particular cases of (1). In this sense, for f (u) = u 2 /2, constant and g = 0, Equation (1) is KS equation, and in [1] exact travelling wave solutions are obtained using trigonometric functions expansions method. In [4,5], the authors have analysed the classical and nonclassical symmetries of Equation (1) with = k, = = 0, g(u) = 0, f (u) constant and u = F(u).…”

Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation

“…On the other hand, in [3] exact solutions are obtained by using trigonometric function expansion method, exact travelling wave solutions have been obtained also in [4] by a generalized F-expansion method and, moreover, in [5] the rst available numerical solutions are obtained by an homotopy analysis method.…”