An application of the ADM to seven-order Sawada–Kotara equations

摘要

We implemented the Adomian decomposition method (for short, ADM) for approximating the solution of the seventh-order Sawada–Kotera (for short, sSK) and a Lax's seventh-order KdV (for short, LsKdV) equations. By using this scheme, explicit exact solution is calculated. We obtain the exact solitary-wave solutions and numerical solutions of the LsKdV and sSK equations for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the both seven-order equations.