The Homotopy analysis method is applied to obtain the approximate solution of the Klein–Gordon–Schrödinger equation. The Homotopy analysis solutions of the Klein–Gordon–Schrödinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.

In this paper, approximate solution of the Sinh-Gordon equation is obtained via the homotopy analysis method. The obtained solution contains an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions.