Wave solutions to the combined KdV-mKdV equation via two methods with the Riccati equation
คำสำคัญ:
the simple equation method with the Riccati equation, the modified extended tanh-function method, he combined KdV-mKdV equation, partial differential equationบทคัดย่อ
The exact traveling wave solutions of the combined kdv-mkdv equation, which are the partial differential equations, were examined using the simple equation method with the Ricci equation and the modified extended tanh-function method. The solutions of the combined kdv-mkdv equation are obtained in terms of hyperbolic functions and trigonometric functions. Some solutions are created in the form of kink waves, which are represented by the two-dimensional graph, the three-dimensional graph, and the contour graph.
เอกสารอ้างอิง
Abdel-Gawad, H. I., Tantawy, M., & Abdelwahab, A. M. (2023). A new technique for solving Burgers-Kadomtsev-Petviashvili equation with an external source. Suppression of wave breaking and shock wave.Alexandria Engineering Journal,69, 167-176. https://doi.org/10.1016/j.aej.2022.12.022
Akbar, M. A., Ali, N. H. M., & Roy, R. (2018). Closed form solutions of two time fractional nonlinear wave equations.Results in Physics,9(1), 1031-1039. https://doi.org/10.1016/j.rinp.2018.03.059
Bashar, M. H., Mawa, H. Z., Biswas, A., & et al.(2023). The modified extended tanh technique ruled to exploration of soliton solutions and fractional effects to the time fractional couple Drinfel'd–Sokolov–Wilsonequation.Heliyon,9(5). https://doi.org/10.1016/j.heliyon.2023.e15662
Ekici, M., & Ünal, M. (2022). Application of the rational (G'/G)-expansion method for solving some coupled and combined wave equations.Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics,71(1), 116-132. https://doi.org/10.31801/cfsuasmas.884025
El-Wakil, S. A., & Abdou, M. A. (2007). Modified extended tanh-function method for solving nonlinear partial differential equations.Chaos, Solitons & Fractals,31(5), 1256-1264. https://doi.org/10.1016/j.chaos.2005.10.072
El-Wakil, S. A., & Abdou, M. A. (2007). New exact travelling wave solutions using modified extended tanh-function method.Chaos, Solitons & Fractals,31(4), 840-852. https://doi.org/10.1016/j.chaos.2005.10.032
He, J. H., & Wu, X. H. (2006). Exp-function method for nonlinear wave equations.Chaos, Solitons & Fractals,30(3), 700-708. https://doi.org/10.1016/j.chaos.2006.03.020
Hu, H., Tan, M., & Hu, X. (2016). New interaction solutions to the combined KdV–mKdVequation from CTE method.Journal of the Association of Arab Universities for Basic and Applied Sciences,21, 64-67. https://doi.org/10.1016/j.jaubas.2016.01.005
Huang, Y., Wu, Y., Meng, F., & Yuan, W. (2014). All exact traveling wave solutions of the combined KdV-mKdV equation.Advances in Difference Equations,2014(1), 1-11. https://doi.org/10.1186/1687-1847-2014-261
Khan, K., Mudaliar, R. K., & Islam, S. R. (2023). Traveling waves in two distinct equations: the (1+1)-Dimensional cKdV–mKdVequation and the sinh-Gordon equation.International Journal of Applied and Computational Mathematics, 9(3), 21. https://doi.org/10.1007/s40819-023-01503-9
Kumar, A., & Pankaj, R. D. (2015). Tanh–cothscheme for traveling wave solutions for Nonlinear Wave Interaction model.Journal of the Egyptian Mathematical Society,23(2), 282-285. http://dx.doi.org/10.1016/j.joems.2014.05.002
Lu, D. &Shi, Q. (2010). New solitary wave solutions for the cKdV–mKdV equation. Journal of Information and Computational Science, 8(7), 1733–1737.
Naher, H., & Abdullah, F. A. (2012). Some new solutions of the combined KdV-MKdV equation by using the improved (G'/G)-expansion method.World Applied Sciences Journal, 16(11), 1559-1570.
Nofal, T. A. (2016). Simple equation method for nonlinear partial differential equations and its applications.Journal of the Egyptian Mathematical Society,24(2), 204-209. https://doi.org/10.1016/j.joems.2015.05.006
Raslan, K. R., EL-Danaf, T. S., & Ali, K. K. (2017). New exact solution of coupled general equal width wave equation using sine-cosine function method.Journal of the Egyptian Mathematical Society,25(3), 350-354. https://doi.org/10.1016/j.joems.2017.03.004
Sanjun, J., & Chankaew, A.(2022). Wave solutions of the DMBBM equation and the cKG equation using the simple equation method.Frontiers in Applied Mathematics and Statistics,8(1), 952668. https://doi.org/10.3389/fams.2022.952668
Thadee, W., & Phoosree, S. (2024). New Wave Behaviors Generated by Simple Equation Method with Riccati Equation of Some Fourth-Order Fractional Water Wave Equations.Journal of the Physical Society of Japan,93(1), 014002. https://doi.org/10.7566/JPSJ.93.014002
Yang, X. F., Deng, Z. C., & Wei, Y. (2015). A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application.Advances in Difference equations,2015, 1-17. https://doi.org/10.1186/s13662-015-0452-4
Yuan, R. R., Shi, Y., Zhao, S. L., & et al. (2023). The combined KdV-mKdV equation: Bilinear approach and rational solutions with free multi-parameters.Results in Physics,55, 107188. https://doi.org/10.1016/j.rinp.2023.107188
Zahran, E. H., & Khater, M. M. (2016). Modified extended tanh-function method and its applications to the Bogoyavlenskii equation.Applied Mathematical Modelling,40(3), 1769-1775. https://doi.org/10.1016/j.apm.2015.08.018
Zahran, E. H., & Khater, M. M. (2016). Modified extended tanh-function method and its applications to the Bogoyavlenskii equation.Applied Mathematical Modelling,40(3), 1769-1775. https://doi.org/10.1016/j.apm.2015.08.018
ดาวน์โหลด
เผยแพร่แล้ว
ฉบับ
ประเภทบทความ
หมวดหมู่
สัญญาอนุญาต
ลิขสิทธิ์ (c) 2024 Journal of Applied Science and Emerging Technology

อนุญาตภายใต้เงื่อนไข Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.