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
By using this method, we obtain abundant new types of exact traveling wave solutions.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, the auxiliary ordinary differential equation is employed to solve the perturbed Klein-Gordon equation with quadratic nonlinearity in the (1+1)-dimension without local inductance and dissipation effect.
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Key Findings & Data:In this paper, the auxiliary ordinary differential equation is employed to solve the perturbed Klein-Gordon equation with quadratic nonlinearity in the (1+1)-dimension without local inductance and dissipation effect.
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Conclusion & Impact:By using this method, we obtain abundant new types of exact traveling wave solutions.
In this paper, the auxiliary ordinary differential equation is employed to solve the perturbed Klein-Gordon equation with quadratic nonlinearity in the (1+1)-dimension without local inductance and dissipation effect. By using this method, we obtain abundant new types of exact traveling wave solutions.
Özet
In this paper, the auxiliary ordinary differential equation is employed to solve the perturbed Klein-Gordon equation with quadratic nonlinearity in the (1+1)-dimension without local inductance and dissipation effect. By using this method, we obtain abundant new types of exact traveling wave solutions.
ZHANG, Z. (2013). 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, Cilt: 37 - Sayı: 2, 259–267. https://ajindex.com/articles/724006
Z. Y. Zhang, Z. H. Liu, X. J. Miao and Y. Z. Chen, Appl. Math. Comput., 216, (2010), 3064. Z. Y. Zhang, Turk. J. Phys., 32, (2008), 235. Z. Y. Zhang, Y. X. Li, Z. H. Liu and X. J. Miao, Commun. Nonlinear Sci. Numer. Simulat., 16, (2011), 3097. Z. Y. Zhang, Z. H. Liu, X. J. Miao and Y. Z. Chen, Phys. Lett. A, 375, (2011), 1275. X. J. Miao and Z. Y. Zhang, Commun. Nonlinear Sci. Numer. Simulat., 16, (2011), 4259. Z. Y. Zhang, X. Y. Gan and D. M. Yu, Z. Naturforsch., 66a, (2011), 721. A. Y ı ldı r ı m and Z. P ı nar, Comput. Math. Appl., 60, (2010), 1873. T. ¨ Ozis and A. Y ı ldı r ı m, Chaos, Solitons and Fractals, 38, (2008), 209. S. T. Mohyud-Din and A. Y ı ldı r ı m, Z. Naturforsch., 65a, (2010), 1077. A. Y ı ldı r ı m, Z. Naturforsch., 63a, (2008), 621. A. Y ı ldı r ı m, S. T. Mohyud-Din and D. H. Zhang, Comput. Math. Appl., 59, (2010), 2473. S. T. Mohyud-Din and A. Y ı ldı r ı m, Z. Naturforsch., 65a, (2010), 1045. A. Y ı ldı r ı m, Z. Naturforsch., 65a, (2010), 418. W. X. Ma and B. Fuchssteiner, Int. J. Nonlinear Mechanics, 31, (1996), 329. W. X. Ma, T. W. Huang and Y. Zhang, Phys. Scr., 82, (2010), 065003. W. X. Ma and Z. N. Zhu, Appl. Math. Computat., 218, (2012), 11871. W. X. Ma and J. H. Lee, Chaos, Solitons and Fractals, 42, (2009), 1356. W. X. Ma and M. Chen, Appl. Math. Comput., 215, (2009), 2835. W. X. Ma and Y. You, Trans. Amer. Math. Soc., 357, (2005), 1753. W. X. Ma, C. X. Li and J. S. He, Nonlinear Anal. TMA, 70, (2009), 4245. W. X. Ma and E. G. Fan, Comput. Math. Appl., 61, (2011), 950. W. X. Ma, Y. Zhang, Y. N. Tang and J. Y. Tu, Appl. Math. Computat., 218, (2012), 7714. A. Biswas, C. Zony and E. Zerrad, Appl. Math. Comput., 203, (2008), 153. R. Sassaman and A. Biswas, Physics Express, 1, (2011), 9. Z. Y. Zhang and X. J. Miao, Comput. Math. Appl., 59, (2010), 1003. Z. Y. Zhang, Z. H. Liu, X. J. Miao and Y. Z. Chen, J. Math. Phys., 52, (2011), 023502. C. E. Xiao and Z. Y. Zhang, Far East J. Appl. Math., 60, (2011), 131. M. A. Aguero, M. L. Najera, J. A. Aguilar and J. Sanchez, Int. J. Theor. Phys., 48, (2009), 2098.
K. C. Basak, P. C. Ray and R. K. Bera, Commun. Nonlinear Sci. Numer. Simulat., 14, (2009), 718. R. Sassaman and A. Biswas, Appl. Math. Computat., 215, (2009), 212. R. Sassaman and A. Biswas, Nonlinear Dyn., 61, (2010), 23. R. Sassaman and A. Biswas, Studies in Math. Sci., 1,(2010), 30. R. Sassaman, A. Heidari, F. Majid and A. Biswas, Dynam. Cont. Discr. Impul. Sys. Series A, 17, (2010), 275. R. Sassaman and A. Biswas, MESA, 2,