Investigation of Analytical Solutions of the Nonlinear Mathematical Model Representing Gas Overflowing

Yıl 2021, Cilt: 11 Sayı: 1, 182 - 190, 30.06.2021

Yusuf Gürefe , Tolga Aktürk

https://doi.org/10.37094/adyujsci.868800

https://izlik.org/JA79AJ73KL

Öz

In this study, traveling wave soliton solutions of hyperbolic and trigonometric functions are successfully obtained by using the modified exponential function method of the Buckley-Leverett equation. In addition to these, there are also rational function solutions. Two and three-dimensional graphs of real and imaginary parts are included with contour simulations to physically analysis of the solution functions of the equation analyzed as a mathematical model using Mathematica software.

Anahtar Kelimeler

Modified exponential function method. , Buckley-Leverett Equation , Traveling wave solution , Modified exponential function method

Kaynakça

• [1] Sun, Y., New travelling wave solutions for Sine-Gordon equation, Journal of Applied Mathematics, 2014.
• [2] Bulut, H., Akturk, T., Gurefe, Y., Traveling wave solutions of the (N+ 1)-dimensional sine-cosine-Gordon equation, American Institute of Physics Conference Proceedings, 1637(1), 145-149, 2014.
• [3] Liu, C. S., Trial equation method and its applications to nonlinear evolution equations, Acta Physica Sinica., 54(6), 2505-2509, 2005.
• [4] Shen, G., Sun, Y., Xiong, Y., New travelling-wave solutions for Dodd-Bullough equation, Journal of Applied Mathematics, 2013.
• [5] Akturk, T., Bulut, H., Gurefe, Y., New function method to the (n+1)-dimensional nonlinear problems, An International Journal of Optimization and Control: Theories & Applications, 7(3), 234-239, 2017.
• [6] Pandir, Y., Gurefe, Y., Kadak, U., Misirli, E., Classification of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstract and Applied Analysis, 2012, 16, 2012.
• [7] Akturk, T., Bulut, H., Gurefe, Y., An application of the new function method to the Zhiber-Shabat equation, An International Journal of Optimization and Control: Theories & Applications, 7(3), 271-274, 2017.
• [8] Chen, Y., Yan, Z., New exact solutions of (2+ 1)-dimensional Gardner equation via the new sine-Gordon equation expansion method, Chaos, Solitons & Fractals, 26(2), 399-406, 2005.
• [9] Kudryashov, N.A., One method for finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, 17, 2248-2253, 2012.
• [10] Sakar, M.G., Saldır, O., Akgül, A., A novel technique for fractional Bagley–Torvik equation, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 89(3), 539-545, 2019.
• [11] Sakar, M.G., Saldır, O., Improving variational iteration method with auxiliary parameter for nonlinear time-fractional partial differential equations, Journal of Optimization Theory and Applications, 174(2), 530-549, 2017.
• [12] Ismael, H.F., Bulut, H., Baskonus, H.M., Gao, W., Newly modified method and its application to the coupled Boussinesq equation in ocean engineering with its linear stability analysis, Communications in Theoretical Physics, 72(11), 115002, 2020.
• [13] Ismael, H.F., Bulut, H., Baskonus, H.M., W-shaped surfaces to the nematic liquid crystals with three nonlinearity laws,. Soft Computing, 25(6), 4513-4524, 2021.
• [14] Ismael, H.F., Baskonus, H.M., Bulut, H., Abundant novel solutions of the conformable Lakshmanan-Porsezian-Daniel model, Discrete & Continuous Dynamical Systems-S, 2020.
• [15] Lingyu, M., Liao, X., Chen, Z., Zou, J., Chu, H., Li, R., Analytical solution of Buckley-Leverett equation for gas flooding including the effect of miscibility with constant- pressure boundary, Energy Exploration & Exploitation, 37.3: 960-991, 2019.
• [16] Bruzón, M.S., Marquez, A.P., Recio, E., Garrido, T.M., de la Rosa, D., Potential systems of a Buckley–Leverett equation: Lie point symmetries and conservation laws, Journal of Mathematical Chemistry, 1-10, 2020.
• [17] Spayd, K.R., Shearer M., The Buckley–Leverett equation with dynamic capillary pressure, SIAM J. Appl. Math., 71, 1088–1108, 2012.
• [18] Hassanizadeh, S. M., Gray, W. G., Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries, Advances in water resources, 13.4, 169-186, 1990.
• [19] Uddin, S., Alam, N., Hossain, S.M.S., Samiu, H., Akbar, M.A., Some new exact traveling wave solutions to the (3+ 1)-dimensional Zakharov-Kuznetsov equation and the burgers equations via Exp-Expansion method, Frontiers of Mathematics and Its Applications, 1.1, 1-8, 2014.