Approximate symmetry and exact solutions of the perturbed nonlinear Klein-Gordon equation

Rahimian, Mohammad; Nadjafikhah, Mehdi

Approximate symmetry and exact solutions of the perturbed nonlinear Klein-Gordon equation

Document Type : Research Paper

Authors

¹ Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran.

² Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology,Narmak, Tehran, 1684613114, Iran

Abstract

In this paper, the Lie approximate symmetry analysis is applied to investigate new exact solutions of the perturbed nonlinear Klein-Gordon equation. The nonlinear Klein-Gordon equation is used to model many nonlinear phenomena. The tanh-coth method, is employed to solve some of the obtained reduced ordinary differential equations. As a result, we construct new analytical solutions with small parameter which is effectively obtained by the proposed method.

Keywords