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