Homotopy analysis method for the Kawahara equation

The homotopy analysis method (HAM) is used to find a family of travelling-wave solutions of the Kawahara equation. This approximate solution, which is obtained as a series of exponentials, has a reasonable residual error. The homotopy analysis method contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of series solution. This method is reliable and manageable. (C) 2008 Elsevier Ltd. All rights reserved.