Modified Camassa–Holm and Degasperis–Procesi Equations Solved by Adomian’s Decomposition Method and Comparison with HPM and Exact Solutions

Many physical and scientific phenomena are modeled by nonlinear partial differential equations (NPDEs); it is difficult to handle nonlinear part of these equations. Recently some analytical methods are applied to solve such equations. In this work, modified Camassa–Holm and Degasperis–Procesi equation is studied. Adomian’s decomposition method (ADM) is applied to obtain solution of this equation. The results are compared to those of homotopy perturbation method (HPM) and exact solution. The study highlights the significant features of the employed method and its ability to handle nonlinear partial differential equations.