An efficient method for analyzing the solutions of the Korteweg-de Vries equation

A new iterative method is applied to study the solutions of the Korteweg-de Vries (KdV) equation. The method is a modified form of the well known Adomian decomposition method (ADM), where it avoids the difficulty of computing the Adomian polynomials. We prove the existence of a unique solution of the KdV equation. And then, we show that the new method generates an infinite series which converges uniformly to the exact solution of the problem. Soliton solutions of the KdV equation are obtained by the new method. Numerical calculations indicate the effectiveness of the new method where the obtained results are very accurate and better than the ones obtained by the ADM.