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

Yıl 2020, Cilt: 10 Sayı: 2, 585 - 594, 30.12.2020
https://doi.org/10.37094/adyujsci.827964

Öz

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.

Kaynakça

  • [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

Yıl 2020, Cilt: 10 Sayı: 2, 585 - 594, 30.12.2020
https://doi.org/10.37094/adyujsci.827964

Öz

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.

Kaynakça

  • [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.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Matematik
Yazarlar

Serbay Duran 0000-0002-3585-8061

Yayımlanma Tarihi 30 Aralık 2020
Gönderilme Tarihi 18 Kasım 2020
Kabul Tarihi 10 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 2

Kaynak Göster

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. Aralık 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, sy. 2 (Aralık 2020): 585-94. https://doi.org/10.37094/adyujsci.827964.
EndNote Duran S (01 Aralık 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, c. 10, sy. 2, ss. 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 (Aralık 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, c. 10, sy. 2, 2020, ss. 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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