Research Article
Year 2021,
Volume: 11 Issue: 1, 182 - 190, 30.06.2021
Abstract
References
- [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.
Investigation of Analytical Solutions of the Nonlinear Mathematical Model Representing Gas Overflowing
Abstract
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.
Keywords
Modified exponential function method. Buckley-Leverett Equation Traveling wave solution Modified exponential function method
References
- [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.
There are 19 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Applied Mathematics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | June 30, 2021 |
| Submission Date | January 26, 2021 |
| Acceptance Date | May 28, 2021 |
| Published in Issue | Year 2021 Volume: 11 Issue: 1 |
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