Version 1
: Received: 24 June 2022 / Approved: 27 June 2022 / Online: 27 June 2022 (03:23:06 CEST)
How to cite:
Babajanov, B.; Abdikarimov, F. Traveling Wave Solutions of the Loaded Non-linear Klein-Gordon Equation via Functional Variable Method. Preprints2022, 2022060344. https://doi.org/10.20944/preprints202206.0344.v1
Babajanov, B.; Abdikarimov, F. Traveling Wave Solutions of the Loaded Non-linear Klein-Gordon Equation via Functional Variable Method. Preprints 2022, 2022060344. https://doi.org/10.20944/preprints202206.0344.v1
Babajanov, B.; Abdikarimov, F. Traveling Wave Solutions of the Loaded Non-linear Klein-Gordon Equation via Functional Variable Method. Preprints2022, 2022060344. https://doi.org/10.20944/preprints202206.0344.v1
APA Style
Babajanov, B., & Abdikarimov, F. (2022). Traveling Wave Solutions of the Loaded Non-linear Klein-Gordon Equation via Functional Variable Method. Preprints. https://doi.org/10.20944/preprints202206.0344.v1
Chicago/Turabian Style
Babajanov, B. and Fakhriddin Abdikarimov. 2022 "Traveling Wave Solutions of the Loaded Non-linear Klein-Gordon Equation via Functional Variable Method" Preprints. https://doi.org/10.20944/preprints202206.0344.v1
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.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
