TY - JOUR
T1 - The Homotopy Perturbation Method and the Adomian Decomposition Method for the Nonlinear Coupled Equations
AU - Elsayed M. E. Zayed  & H. M. Abdel Rahman 
JO - Journal of Partial Differential Equations
VL - 4
SP - 334
EP - 351
PY - 2009
DA - 2009/11
SN - 22
DO - http://doi.org/10.4208/jpde.v22.n4.3
UR - https://global-sci.org/intro/article_detail/jpde/5261.html
KW - Homotopy perturbation method
KW - Adomian decomposition method
KW - coupled Korteweg-de Vries equations
KW - shallow water equations
AB - <p>In this paper, we have used the homotopy perturbation and the Adomian decomposition methods to study the nonlinear coupled Kortewge-de Vries and shallow water equations. The main objective of this paper is to propose alternative methods of solutions, which do not require small parameters and avoid linearization and physical unrealistic assumptions. The proposed methods give more general exact solutions without much extra effort and the results reveal that the homotopy perturbation and the Adomian decomposition methods are very effective, convenient and quite accurate to the systems of coupled nonlinear equations.</p>