New Path of Popularized Homogeneous Balance Method and Travelling Wave Solutions of a Nonlinear Klein-Gordon Equation

Israa A.  Ibrahim; Raad A.  Hameed; Wafaa M.  Taha; Maan A.  Rasheed

doi:10.24996/ijs.2022.63.6.31

Authors

Israa A. Ibrahim General Directorate of Kirkuk Province Education, Ministry of Education, Kirkuk, Iraq
Raad A. Hameed Department of Mathematics, College of Education for Pure Science, Tikrit University, Tikrit, Iraq https://orcid.org/0000-0001-9500-8563
Wafaa M. Taha Department of Mathematics, College of Science, University of Kirkuk, Kirkuk, Iraq
Maan A. Rasheed Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.6.31

Keywords:

Klein–Gorden equation, Traveling wave, Homogeneous balance method, NLEEs

Abstract

The aim of this paper is to obtain a set of traveling wave solutions for klein –Gorden equation with kerr law non-linearity. More precisely, we apply a new path of popularized homogeneous balance (HB) method in terms of using linear auxiliary equations to find the results of non-linear klein-Gorden equation, which is a fundamental approach to determine competent solutions. The solutions are achieved as the integration of exponential, hyperbolic, trigonometric and rational functions. Besides, some of the solutions are demonstrated by the3D graphics.