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Traveling Wave Solutions of the Loaded Non-linear Klein-Gordon Equation via Functional Variable Method

This version is not peer-reviewed.

Submitted:

24 June 2022

Posted:

27 June 2022

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Abstract
In this paper, the functional variable method is used to establish solitary wave solutions and periodic wave solutions of the loaded quadratic non-linear Klein-Gordon equation, the loaded cubic non-linear Klein-Gordon equation and the loaded coupled non-linear Klein-Gordon equation. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab software. The main advantage of the proposed functional variable method over other methods is that it provides more new exact traveling wave solutions along with additional free parameters. The graphical representations of the soliton solutions and the periodic wave solutions by using distinct values of random parameter are demonstrated to better understand their physical features. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena.
Keywords: 
loaded Klein-Gordon equation; periodic solutions; functional variable method; trigonometric function; soliton solutions; hyperbolic function
Subject: 
Computer Science and Mathematics  -   Applied Mathematics
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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