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 ħħ, which provides us with a simple way to adjust and control the convergence region of series solution. This method is reliable and manageable.