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.