The Method of Lines and Adomian Decomposition for Obtaining Solitary Wave Solutions of the KdV Equation

The method of lines (MOL) and Adomian decomposition method (ADM) are presented for obtaining solitary wave solutions of the korteweg-de Varies equation (KdV). The numerical results of the MOL are compared with the analytical results of the ADM. The method of lines gives accurate results over the Adomian method. In order to show the reliability of the considered methods we have compared the obtained solutions with the exact ones. The results reveal that the method of lines is more effective and convenient than the Adomian decomposition method for solving such type of partial differential equations.