Exact solutions for the generalized Klein-Gordon equation via a transformation and Exp-function method and comparison with Adomian's method

Authors:
A. Ebaid
Affiliations:
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Hiliopolis, Cairo, Egypt
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 4
Cited 2

A decomposition method for solving the nonlinear Klein-Gordon equation

Journal of Computational Physics
A reliable modification of Adomian decomposition method

Applied Mathematics and Computation
The modified decomposition method applied to unsteady flow of gas through a porous medium

Applied Mathematics and Computation
Decomposition methods: A new proof of convergence

Mathematical and Computer Modelling: An International Journal

A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method

Journal of Computational and Applied Mathematics
New types of exact solutions for nonlinear Schrödinger equation with cubic nonlinearity

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper, a suitable transformation and a so-called Exp-function method are used to obtain different types of exact solutions for the generalized Klein-Gordon equation. These exact solutions are in full agreement with the previous results obtained in Refs. [Sirendaoreji, Auxiliary equation method and new solutions of Klein-Gordon equations, Chaos, Solitons & Fractals 31 (4) (2007) 943-950; Huiqun Zhang, Extended Jacobi elliptic function expansion method and its applications, Communications in Nonlinear Science and Numerical Simulation, 12 (5) (2007) 627-635]. One of these exact solutions is compared with the approximate solutions obtained by the modified decomposition method. Accurate numerical results for a wider range of time are obtained after using different types of ADM-Pade approximation. Our results show that the Exp-function method is very effective in finding exact solutions for the problem considered while the modified decomposition method is very powerful in finding numerical solutions with good accuracy for nonlinear PDE without any need for a transformation or perturbation.