NEW EXACT SOLUTIONS FOR KLEIN-GORDON EQUATION

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 with the aid of wave transform. Then we obtained various new exact solutions via the method. These solutions can play an important role in engineering and physics. For some solutions, we drew two and three-dimensional graphics to understand physical behaviors. We performed all the calculations and graphs in this article by Wolfram Mathematica.

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[1] Akın, L ., “A Characterization of Approximation of Hardy Operators in VLS”. Celal Bayar University Journal of Science, 14 (3), 333-336,2018. DOI: 10.18466/cbayarfbe.449954.

[2] Mamedov, F, Zeren, Y, Akın, L, “Compactification of weighted Hardy operator in variable exponent Lebesgue spaces”, Asian Journal of Mathematics and Computer Science, 17:1, 38- 47,2017.

[3] Akın, L. “On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces” Universal Journal of Mathematics and Applications, 2 (3), 148- 151,2019. DOI: 10.32323/ujma.522420

[4] Cruz-Uribe, D., Diening, L. and Hasto, P., “The maximal operator on weighted variable Lebesgue spaces”, Fract. Calc. Appl. Anal. 14(3), 361-374,2011.

[5] Biswas, A., Zony, C. and Zerrad, E., “Soliton perturbation theory for the quadratic nonlinear Klein–Gordon equation” Applied Mathematics and Computation, 203, 153, 2008.

[6] 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.

[7] 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.

[8] Zhang, Z., “New Exact Traveling Wave Solutions for the Nonlinear Klein-Gordon Equation”, Turkish Journal of Physics, 32, 235-240,2008.

[9] 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.

[10] 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.

[11] 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.

[12] 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.

[13] 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.

[14] Düşünceli, F. “Solutions for the Drinfeld-Sokolov Equation Using an IBSEFM Method”, MSU Journal of Science, 6(1), 505-510,2018.

[15] 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.

[16] 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.

[17] 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.