NEW EXACT SOLUTIONS FOR THE KLEIN-GORDON EQUATION

Year 2020, Volume: 6 Issue: 2, 78 - 84, 29.12.2020

Faruk Düşünceli

Abstract

In this paper, we applied the improved Bernoulli sub-equation function method for the Klein-Gordon equation. Firstly, we reduced the equation to a nonlinear ordinary differential equation by the aid of wave transform. Then we have been obtained various new exact solutions via the method. For some solutions, we drew two and three-dimensional graphics to understand physical behaviors. Nonlinear evolution equations (NLEEs) are widely used because it finds application in many nonlinear disciplines such as plasma physics, optical fibers, fluid mechanics, fluid dynamics and so on. One of the best known of these equations is Klein-Gordon equation(KGE).

Keywords

Klein-Gordon Equation, Improved Bernoulli sub-equation function method, Exact solutions

References

• [1] Biswas, A., Zony, C. and Zerrad, E., “Soliton perturbation theory for the quadratic nonlinear Klein–Gordon equation” Applied Mathematics and Computation, 203, 153, 2008.
• [2] Sassaman, R., Biswas, A, “Soliton perturbation theory for phi-four model and nonlinear Klein–Gordon equations”, Commun Nonlinear Sci Numer Simulat, 14, 3239-3249, 2009.
• [3] Zhang,Z., “Exact traveling wave solutions of the perturbed Klein–Gordon equation with quadratic nonlinearity in (1+1)-dimension,Part I: Without local inductance and dissipation effect” , Turkish Journal of Physics, 37, 259-267,2013.
• [4] Zhang,Z., “New Exact Traveling Wave Solutions for the Nonlinear Klein-Gordon Equation” , Turkish Journal of Physics, 32, 235-240,2008.
• [5] Wazwaz, A. M. “The tanh and sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation”, Applied Mathematics and Computation, 167(2), 1179–1195, 2005.
• [6] Hafez, M. G., Nur Alam, M. and Akbar, M.A. “Exact traveling wave solutions to the Klein–Gordon equation using the novel (G0/G)-expansion method” , Results in Physics, 4, 177-184, 2014.
• [7] Yindoula, J.B., Massamba, A. and Bissanga, G., “Solving of Klein-Gordon by Two Methods of Numerical Analysis” , Journal of Applied Mathematics and Physics, 4, 1916-1929,2016.
• [8] Shahen, N.H.M., Foyjonnesa and Habibul Bashar, Md. “Exploration on traveling wave solutions to the 3rd-order klein–fock-gordon equation (KFGE) in mathematical physics” , International Journal of Physical Research, 8(1), 14-21,2019.
• [9] Baskonus H.M., Bulut H. “On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method”, Waves in Randomand Complex Media. 25(4) 720-728. 2015.
• [10] Düşünceli, F. “Solutions for the Drinfeld-Sokolov Equation Using an IBSEFM Method”, MSU Journal of Science, 6(1), 505-510,2018.
• [11] Düşünceli ,F. “New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model”, Advances in Mathematical Physics, , Article ID 7801247, 9 pages, 2019. https://doi.org/10.1155/2019/7801247.
• [12] Düşünceli, F. “New Exact Solutions for the (3 + 1) Dimensional B-type Kadomtsev-Petviashvili Equation”. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12 (1), 463-468, 2019.
• [13] Düşünceli,F. Çelik, E., Aşkın, M. and Bulut, H. “New Exact Solutions for the Doubly Dispersive Equation Using an Improved Bernoulli Sub-Equation Function Method”, Indian Journal of Physics, 1-6, 2020.