Abstract
In the present study, by implementing the direct algebraic method, we present the traveling wave solutions for some differentkinds of the Korteweg-de Vries ( KdV) equations. The exact solutions of the Kawahara, fifth order KdV and generalized fifth orderKdV equations are obtained. Solutions for the Kawahara, fifth order KdV and generalized fifth order KdV equations are obtainedprecisely and efficiency of the method can be demonstrated. The stability of these solutions and the movement role of the waves bymaking the graphs of the exact solutions are analyzed. All solutions are exact and stable, and have applications in physics. (C) 2016 The Authors. Production and hosting by Elsevier B. V. on behalf of Taibah University. This is an open access article underthe CC BY-NC-ND license.