An application of the MEFM to the modified Boussinesq equation

In this paper, some travelling wave solutions of the Modified Boussinesq (MBQ)equation are obtained by using the modified expansion function method (MEFM).When the obtained solutions are commented, trigonometric functions includinghyperbolic features are obtained. The 2D and 3D graphics of the solutions havebeen investigated by selecting appropriate parameters. All the obtained solutionsprovide the MBQ equation. In this work, all mathematical calculations are donewith Wolfram Mathematica software.

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Liu, C. S. (2005). Trial equation method and its applications to nonlinear evolution equations, Acta Physica Sinica, 54(6), 2505-2509.
Shen, G., Sun, Y., & Xiong, Y. (2013). New travelling-wave solutions for Dodd-Bullough equation, Journal of Applied Mathematics, vol. 2013, Article ID 364718, 5 pages.
Sun, Y. (2014). New travelling wave solutions for Sine-Gordon equation, Journal of Applied Mathematics, vol. 2014, Article ID 841416, 4 pages.
Bulut, H., Akturk, T., & Gurefe, Y. (2015). Travelling wave solutions of the (N+1)-dimensional sine-cosine-Gordon equation, AIP Conference Proceedings 1637, 145.
Akturk, T., Bulut, H., & Gurefe, Y. (2017). New function method to the (n+1)-dimensional nonlinear problems, An International Journal of Optimization and Control: Theories & Applications, 7(3), 234- 239.
Akturk, T., Bulut, H., & Gurefe, Y. (2017). 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.
Pandir, Y., Gurefe, Y., Kadak, U., & Misirli, E. (2012). Classification of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstract and Applied Analysis, vol. 2012, Article ID 478531, 16 pages.
Kudryashov, N. A. (2012). One method for finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, 17(6), 2248-2253.
Chen, Y., & Yan, Z. (2005). New exact solutions of (2+ 1)-dimensional Gardner equation via the new sine-Gordon equation expansion method. Chaos, Solitons & Fractals, 26(2), 399-406.
Baskonus, H. M., Bulut, H., & Sulaiman, T. A. (2017). Investigation of various travelling wave solutions to the extended (2+1)-dimensional quantum ZK equation. The European Physical Journal Plus, 132(11), 482.
Baskonus, H. M., Bulut, H., & Atangana, A. (2016). On the complex and hyperbolic structures of the longitudinal wave equation in a magneto-electro- elastic circular rod. Smart Materials and Structures, 25(3), 035022.
He, J. H., & Wu, X. H. (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, 30(3), 700-708.
Xu, F. (2008). Application of Exp-function method to symmetric regularized long wave (SRLW) equation. Physics Letters A, 372(3), 252-257.
Clarkson, P.A. (1986). The Painleve property, a modified Boussinesq equation and a modified Kadomtsev–Petviashvili equation. Physica D: Nonlinear Phenomena, 19(3), 447–450.
Li, S., Zhang, W., & Bu, X. (2017). Periodic wave solutions and solitary wave solutions of generalized modified Boussinesq equation and evolution relationship between both solutions. Journal of Mathematical Analysis and Applications, 449(1), 96-126.
Levine, H.A., Sleeman, B.D. (1985). A note on the nonexistence of global solutions of initial boundary value problems for the Boussinesq equation, Journal of Mathematical Analysis and Applications, 107, 206–210.
Naher, H., & Abdullah, F. A. (2013). New approach of (G′/G)-expansion method and new approach of generalized (G′/G)-expansion method for nonlinear evolution equation. American Institute of Physics Advances, 3(3), 032116.