An application of the decomposition method for the generalized KdV and RLW equations

We consider solitary-wave solutions of the generalized regularized long-wave (RLW) and Korteweg-de Vries (KdV) equations. We prove the convergence of Adomian decomposition method applied to the generalized RLW and KdV equations. Then we obtain the exact solitary-wave solutions and numerical solutions of the generalized RLW and KdV equations for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the generalized RLW and KdV equations.