The homotopy analysis method (HAM) is
used to find a family of solitary solutions of the
Kuramoto–Sivashinsky 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 , which
provides us with a simple way to adjust and control the
convergence region of series solution. This method is
reliable and manageable.
