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Birleştirilmiş Konno-Oono Denkleminin Fonksiyonel Değişken Metodu ve İki Değişkenli (G'/G,1/G)-Açılım Metodu Yardımıyla Solitary Dalga Çözümleri

Year 2020, , 585 - 594, 30.12.2020
https://doi.org/10.37094/adyujsci.827964

Abstract

Bu çalışmada, birleştirilmiş Konno-Oono Denkleminin fonksiyonel değişken metodu ve iki değişkenli (G'/G,1/G)- açılım metodu yardımıyla solitary dalga çözümlerini araştırdık. Ele aldığımız denklemin trigonometrik ve hiperbolik ve rasyonel fonksiyon formunda solitary dalga çözümlerini elde ettik. Ayrıca Mathematica 7 yardımıyla bazı çözümlerin iki ve üç boyutlu grafiklerini çizdik.

References

  • [1] Wang, M., Li, X., Zhang, J., The (G^'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A, 372, 417-423, 2008.
  • [2] Guo, S., Zhou, Y., Zhao, X., The extended (G^'/G)-expansion method and its applications to the Whitham-Broer-Kaup-Like equations and coupled Hirota-Satsuma KdV equations, Applied Mathematics and Computation, 215, 3214-3221, 2010.
  • [3] Lü, H.L., Liu, X.Q., Niu, L., A generalized (G^'/G)-expansion method and its applications to nonlinear evolution equations, Applied Mathematics and Computation, 215, 3811-3816, 2010.
  • [4] Malfiet, W., Solitary wave solutions of nonlinear wave equations, American Journal of Physics, 60, 650-654, 1992.
  • [5] He, J.H., Wu, X.H., Exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals, 30, 700-708, 2006.
  • [6] Ozpinar, F., Baskonus, H.M., Bulut, H., On the Complex and Hyperbolic Structures for the (2+1)-Dimensional Boussinesq Water Equation, Entropy, 17(12), 8267-8277, 2015.
  • [7] Baskonus, H.M., Askin, M., Travelling Wave Simulations to the Modified Zakharov-Kuzentsov Model Arising In Plasma Physics. 6th International Youth Science Forum “LITTERIS ET ARTIBUS” Comput. Sci. and Eng. 2016.
  • [8] Baskonus, H.M., Sulaiman, T.A., Bulut, H., On the Novel Wave Behaviors to the Coupled Nonlinear Maccari's System with Complex Structure, Optik, 131, 1036-1043, 2017.
  • [9] Bulut, H., Sulaiman, T.A., Baskonus, H.M., New Solitary and Optical Wave Structures to the Korteweg-de Vries Equation with Dual-Power Law Nonlinearity, Optical and Quantum Electronics, 48, 1-14, 2016.
  • [10] Gao, W., Baskonus, H. M., Shi, L., New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system, Advances in Difference Equations, 391, 1-11, 2020.
  • [11] Gao, W., Yel, G., Baskonus, H. M., Cattani, C., Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation, Aims Mathematics, 5(1), 507–521, 2020.
  • [12] Zerarka, A., Ouamane, S., On the functional variable method for finding exact solutions to a class of wave equations, Applied Mathematics and Computation, 217, 2897–2904, 2010.
  • [13] Li, L., Li, E., Wang, M., The (G′/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations, Applied Mathematics-A Journal of Chinese Universities, 25, 454–462, 2010.
  • [14] Konno, K., Oono, H., New coupled integrable dispersionless equations, Journal of the Physical Society of Japan, 63, 377–378, 1994.
  • [15] Manafian, J., Zamanpourand, I., Ranjbaran, A., On some new analytical solutions for new coupled Konno–Oono equation by the external trial equation method, Journal of Physics Communications, 2, 015023, 2018.
  • [16] Bashar, A., Mondal, G., Khan, K., Bekir, A., Traveling wave solutions of new coupled Konno-Oono equation, New Trends in Mathematical Sciences, 4, 296-303, 2016.
  • [17] Torvattanabun, M., Juntakud, P., Saiyun, A., Khansai, N., The new exact solutions of the new coupled konno-oono equation by using extended simplest equation method, Applied Mathematical Sciences, 12, 293-301, 2018.
  • [18] Inan, E., Multiple soliton solutions of some nonlinear partial differential equations, Universal Journal of Mathematics and Applications, 1, 273-279, 2018.

Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G'/G,1/G) -Expansion Method

Year 2020, , 585 - 594, 30.12.2020
https://doi.org/10.37094/adyujsci.827964

Abstract

In this work, we investigate solitary wave solutions of the coupled Konno-Oono equation with the aid of the functional variable method (FVM) and the two variables (G'/G,1/G)-expansion method. We obtain solitary wave solutions in form of trigonometric function and hyperbolic function and rational function solutions. We also draw two and three-dimensional graphics for some solutions with help of Mathematica 7.

References

  • [1] Wang, M., Li, X., Zhang, J., The (G^'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A, 372, 417-423, 2008.
  • [2] Guo, S., Zhou, Y., Zhao, X., The extended (G^'/G)-expansion method and its applications to the Whitham-Broer-Kaup-Like equations and coupled Hirota-Satsuma KdV equations, Applied Mathematics and Computation, 215, 3214-3221, 2010.
  • [3] Lü, H.L., Liu, X.Q., Niu, L., A generalized (G^'/G)-expansion method and its applications to nonlinear evolution equations, Applied Mathematics and Computation, 215, 3811-3816, 2010.
  • [4] Malfiet, W., Solitary wave solutions of nonlinear wave equations, American Journal of Physics, 60, 650-654, 1992.
  • [5] He, J.H., Wu, X.H., Exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals, 30, 700-708, 2006.
  • [6] Ozpinar, F., Baskonus, H.M., Bulut, H., On the Complex and Hyperbolic Structures for the (2+1)-Dimensional Boussinesq Water Equation, Entropy, 17(12), 8267-8277, 2015.
  • [7] Baskonus, H.M., Askin, M., Travelling Wave Simulations to the Modified Zakharov-Kuzentsov Model Arising In Plasma Physics. 6th International Youth Science Forum “LITTERIS ET ARTIBUS” Comput. Sci. and Eng. 2016.
  • [8] Baskonus, H.M., Sulaiman, T.A., Bulut, H., On the Novel Wave Behaviors to the Coupled Nonlinear Maccari's System with Complex Structure, Optik, 131, 1036-1043, 2017.
  • [9] Bulut, H., Sulaiman, T.A., Baskonus, H.M., New Solitary and Optical Wave Structures to the Korteweg-de Vries Equation with Dual-Power Law Nonlinearity, Optical and Quantum Electronics, 48, 1-14, 2016.
  • [10] Gao, W., Baskonus, H. M., Shi, L., New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system, Advances in Difference Equations, 391, 1-11, 2020.
  • [11] Gao, W., Yel, G., Baskonus, H. M., Cattani, C., Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation, Aims Mathematics, 5(1), 507–521, 2020.
  • [12] Zerarka, A., Ouamane, S., On the functional variable method for finding exact solutions to a class of wave equations, Applied Mathematics and Computation, 217, 2897–2904, 2010.
  • [13] Li, L., Li, E., Wang, M., The (G′/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations, Applied Mathematics-A Journal of Chinese Universities, 25, 454–462, 2010.
  • [14] Konno, K., Oono, H., New coupled integrable dispersionless equations, Journal of the Physical Society of Japan, 63, 377–378, 1994.
  • [15] Manafian, J., Zamanpourand, I., Ranjbaran, A., On some new analytical solutions for new coupled Konno–Oono equation by the external trial equation method, Journal of Physics Communications, 2, 015023, 2018.
  • [16] Bashar, A., Mondal, G., Khan, K., Bekir, A., Traveling wave solutions of new coupled Konno-Oono equation, New Trends in Mathematical Sciences, 4, 296-303, 2016.
  • [17] Torvattanabun, M., Juntakud, P., Saiyun, A., Khansai, N., The new exact solutions of the new coupled konno-oono equation by using extended simplest equation method, Applied Mathematical Sciences, 12, 293-301, 2018.
  • [18] Inan, E., Multiple soliton solutions of some nonlinear partial differential equations, Universal Journal of Mathematics and Applications, 1, 273-279, 2018.
There are 18 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Mathematics
Authors

Serbay Duran 0000-0002-3585-8061

Publication Date December 30, 2020
Submission Date November 18, 2020
Acceptance Date December 10, 2020
Published in Issue Year 2020

Cite

APA Duran, S. (2020). Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G’/G,1/G) -Expansion Method. Adıyaman University Journal of Science, 10(2), 585-594. https://doi.org/10.37094/adyujsci.827964
AMA Duran S. Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G’/G,1/G) -Expansion Method. ADYU J SCI. December 2020;10(2):585-594. doi:10.37094/adyujsci.827964
Chicago Duran, Serbay. “Solitary Wave Solutions of the Coupled Konno-Oono Equation by Using the Functional Variable Method and the Two Variables (G’/G,1/G) -Expansion Method”. Adıyaman University Journal of Science 10, no. 2 (December 2020): 585-94. https://doi.org/10.37094/adyujsci.827964.
EndNote Duran S (December 1, 2020) Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G’/G,1/G) -Expansion Method. Adıyaman University Journal of Science 10 2 585–594.
IEEE S. Duran, “Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G’/G,1/G) -Expansion Method”, ADYU J SCI, vol. 10, no. 2, pp. 585–594, 2020, doi: 10.37094/adyujsci.827964.
ISNAD Duran, Serbay. “Solitary Wave Solutions of the Coupled Konno-Oono Equation by Using the Functional Variable Method and the Two Variables (G’/G,1/G) -Expansion Method”. Adıyaman University Journal of Science 10/2 (December 2020), 585-594. https://doi.org/10.37094/adyujsci.827964.
JAMA Duran S. Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G’/G,1/G) -Expansion Method. ADYU J SCI. 2020;10:585–594.
MLA Duran, Serbay. “Solitary Wave Solutions of the Coupled Konno-Oono Equation by Using the Functional Variable Method and the Two Variables (G’/G,1/G) -Expansion Method”. Adıyaman University Journal of Science, vol. 10, no. 2, 2020, pp. 585-94, doi:10.37094/adyujsci.827964.
Vancouver Duran S. Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G’/G,1/G) -Expansion Method. ADYU J SCI. 2020;10(2):585-94.

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