Series Solutions with Convergence-Control Parameter for Three Highly Non-Linear PDEs: KdV, Kawahara and Gardner equations

Abstract

Here, an analytic method, namely the homotopy analysis method (shortly HAM), is applied to solve the KdV, Kawahara and Gardner equations. The HAM is a strong and easy-to-use analytic tool for nonlinear problems and dose not need small parameters in the equations. This method contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy.