On the solution of the non-linear Korteweg-de Vries equation by the decomposition method

Abstract

The Adomian decomposition method is used to implement the non-linear Korteweg-de Vries equations. The analytic solution of the equation is calculated in the form of a convergent power series with easily computable components. The non-homogeneous problem is quickly solved by observing the self-cancelling noise terms whose sum vanishes in the limit. Comparing this methodology with some known techniques shows that the present approach is highly accurate.