A numerical application of the decomposition method for the combined KdV–MKdV equation

摘要

We consider solitary-wave solutions of the combined Korteweg de Vries–Modified Korteweg de Vries (KdV–MKdV) equation. We prove the convergence of Adomian decomposition method (ADM) applied to the combined KdV–MKdV equation. Then we obtain the exact solitary-wave solutions and numerical solutions of the combined KdV–MKdV equation for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the combined KdV–MKdV equation.