Adaptive control and synchronization of the Newton-Leipnik systems

Abstract

One of the newest analytical methods to solve nonlinear dispersive wave equations is using both homotopy and perturbation methods which is called (HPM). Other the reliable methods are variational iteration method (VIM) by He and Adomian's decomposition method (ADM). Here, we compare the exact solution of HPM which are applied to solve a various fifth-order Korteweg-de Vries problems with initial condition with obtained results of (VIM) and (ADM).Comparison of the results with those obtained by (ADM )and (VIM) reveals that (HPM) is very effective, convenient and quite accurate to both linear and nonlinear problems. It is predicted that (HPM) can be widely applied in engineering.