Applied Sumudu Transform with Adomian Decomposition Method to the Coupled Drinfeld–Sokolov–Wilson System

In this paper, we studied and applied a modern numerical method, which is combining Sumudu transform with Adomian decomposition Method to obtain approximate solutions of the nonlinear the Coupled Drinfeld– Sokolov–Wilson (DSW) system. Positive and negative values of the variable x and various values of the variable t were taken with the initial conditions of the system as well as the values of the parameters . The efficiency of the method was verified, as the results obtained were compared with the accurate solution of the system. We noticed that the results are very accurate and the effectiveness of the method was confirmed.