The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation

Here, an analytic technique, namely the homotopy analysis method (HAM), is applied to solve a generalized Hirota–Satsuma coupled KdV equation. HAM is a strong and easy-to-use analytic tool for nonlinear problems and dose not need small parameters in the equations. Comparison of the results with those of Adomian’s decomposition method (ADM) and homotopy perturbation method (HPM), has led us to significant consequences. The homotopy analysis method contains the auxiliary parameter ¯h, which provides us with a simple way to adjust and control the convergence region of solution series.

Homotopy analysis method; Adomian’s decomposition method; Homotopy perturbation method; Generalized Hirota–Satsuma coupled KdV equation