Application of the optimal homotopy asymptotic method for the solution of the Korteweg–de Vries equation

The Optimal Homotopy Asymptotic Method (OHAM), a semi-analytic approximate technique for the treatment of time-dependent partial differential equations, has been used in this presentation. To see the effectiveness of the method, we consider Korteweg–de Vries (KdV) equation with different initial conditions. It provides us with a convenient way to control the convergence of approximate solutions. The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. The results reveal that the method is explicit.