Zaman Parametresine Bağlı Uyumlu Kesirli Mertebeden Date-Jimbo Kashiwara-Miwa Denkleminin İlerleyen Dalga Çözümleri

Yıl 2024, Cilt: 14 Sayı: 1, 38 - 51, 30.06.2024

Tolga Aktürk Aslı Alkan Hasan Bulut Nesrin Güllüoğlu

https://doi.org/10.54370/ordubtd.1312038

Öz

Bu makalede, uyumlu kesirli türevli Date–Jimbo–Kashiwara–Miwa denkleminin ilerleyen dalga çözümleri, değiştirilmiş üstel fonksiyon yöntemi (DÜFY) ile elde edilmiştir. Bulunan dalga çözümlerinin periyodik fonksiyon özelliği taşıyan fonksiyonlar olduğu görülmüştür. Elde edilen dalga çözümlerindeki parametreler için uygun değerler daha sonra, çözüm fonksiyonlarını simüle eden üç boyutlu iki tane kontur ve yoğunluk grafiklerini oluşturmak için kullanılmaktadır.

Anahtar Kelimeler

Uyumlu Date–Jimbo–Kashiwara–Miwa denklemi, değiştirilmiş üstel fonksiyon metodu, ilerleyen dalga çözümü

The Traveling Wave Solutions of Date–Jimbo–Kashiwara–Miwa Equation with Conformable Derivative Dependent on Time Parameter

Öz

In the paper, the traveling wave solutions of the conformable derivative Date–Jimbo–Kashiwara–Miwa equation were obtained by the modified exponential function method (MEFM). It has been seen that the wave solutions found are functions that have the feature of being periodic functions. The proper values for the parameters in the acquired wave solutions are then used to generate two contour and density graphs in three dimensions that simulate the solution functions.

Anahtar Kelimeler

Conformable Date–Jimbo–Kashiwara–Miwa equation, modified exponential function method, traveling wave solution

Kaynakça

• Abdel-Gawad, H. I., & Osman, M. S. (2013). On the variational approach for analyzing the stability of solutions of evolution equations. Kyungpook mathematical journal, 53(4), 661-680. http://dx.doi.org/10.5666/KMJ.2013.53.4.680
• Abdeljawad, T. (2015). On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, 57-66. https://doi.org/10.1016/j.cam.2014.10.016
• 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. https://doi.org/10.11121/ijocta.01.2017.00488
• Baskonus, H. M., & Bulut, H. (2015). New hyperbolic function solutions for some nonlinear partial differential equation arising in mathematical physics. Entropy, 17(6), 4255-4270. https://doi.org/10.3390/e17064255
• 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. https://doi.org/10.1088/0964-1726/25/3/035022
• 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. https://doi.org/10.1140/epjp/i2017-11778-y
• Chen, Y., & Wang, Q. (2005). Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1+1)-dimensional dispersive long wave equation. Chaos, Solitons & Fractals, 24(3), 745-757. https://doi.org/10.1016/j.chaos.2004.09.014
• 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. https://doi.org/10.1016/j.chaos.2005.01.004
• Dubrovsky, V. G., & Lisitsyn, Y. V. (2002). The construction of exact solutions of two-dimensional integrable generalizations of Kaup–Kuperschmidt and Sawada–Kotera equations via∂ ̄-dressing method. Physics Letters A, 295(4), 198-207. https://doi.org/10.1016/S0375-9601(02)00154-8
• Duran, S. (2020). Exact solutions for time-fractional Ramani and Jimbo—Miwa equations by direct algebraic method. Advanced Science, Engineering and Medicine, 12(7), 982-988. https://doi.org/10.1166/asem.2020.2663
• Duran, S. (2021a). Dynamic interaction of behaviors of time-fractional shallow water wave equation system. Modern Physics Letters B, 35(22), 2150353. https://doi.org/10.1142/S021798492150353X
• Duran, S. (2021b). An investigation of the physical dynamics of a traveling wave solution called a bright soliton. Physica Scripta, 96(12), 125251. https://doi.org/10.1088/1402-4896/ac37a1
• Gözütok, N.Y., & Gözütok, U. (2018). Multivariable conformable fractional calculus. Filomat, 32(2), 45-53. https://doi.org/10.48550/arXiv.1701.00616
• Guo, F., & Lin, J. (2019). Interaction solutions between lump and stripe soliton to the (2+ 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation. Nonlinear Dynamics, 96, 1233-1241. https://doi.org/10.1007/s11071-019-04850-9
• Hossain, A. K. S., & Akbar, M. A. (2017). Closed form solutions of two nonlinear equation via the enhanced (G′/G)-expansion method. Cogent Mathematics, 4(1), 1355958. https://doi.org/10.1080/23311835.2017.1355958
• Ismael, H. F., Seadawy, A., & Bulut, H. (2021). Rational solutions, and the interaction solutions to the (2+ 1)-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation. International Journal of Computer Mathematics, 98(12), 2369-2377. https://doi.org/10.1080/00207160.2021.1897112
• Jafari, H., Kadkhoda, N., & Baleanu, D. (2015). Fractional Lie group method of the time-fractional Boussinesq equation. Nonlinear Dynamics, 81, 1569-1574. https://doi.org/10.1007/s11071-015-2091-4
• Jianming, L., Jie, D., & Wenjun, Y. (2011). Bäcklund transformation and new exact solutions of the Sharma-Tasso-Olver equation. Abstract and Applied Analysis, 2011, 1-8. https://doi.org/10.1155/2011/935710
• Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65-70. https://doi.org/10.1016/j.cam.2014.01.002
• Kubal, Ç., & Aktürk, T. (2023). Investigation of traveling wave solutions of nonlinear mathematical models by the modified exponential function method. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 25(2), 575-598. https://doi.org/10.25092/baunfbed.1244878
• Kumar, A., & Pankaj, R. D. (2015). Tanh–coth scheme for traveling wave solutions for Nonlinear Wave Interaction model. Journal of the Egyptian Mathematical Society, 23(2), 282-285. https://doi.org/10.1016/j.joems.2014.05.002
• Lü, D. (2005). Jacobi elliptic function solutions for two variant Boussinesq equations. Chaos, Solitons & Fractals, 24(5), 1373-1385. https://doi.org/10.1016/j.chaos.2004.09.085
• Malwe, B.H., Betchewe, G., Doka, S.Y., & Kofane, C.T. (2016). Travelling wave solutions and soliton solutions for the nonlinear transmission line using the generalized Riccati equation mapping method. Nonlinear Dynamics, 84, 171–177. https://doi.org/10.1007/s11071-015-2318-4
• Mohyud-Din, S. T., & Noor, M. A. (2007). Homotopy perturbation method for solving fourth-order boundary value problems. Mathematical Problems in Engineering, 2007. http://doi.org/10.1155/2007/98602
• 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. https://doi.org/10.1016/j.joems.2014.03.005
• Salas, A. H., & Gómez S, C. A. (2010). Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation. Mathematical Problems in Engineering, 2010, 194329. https://doi.org/10.1155/2010/194329
• Shen, G., Sun, Y., & Xiong, Y. (2013). New travelling-wave solutions for Dodd-Bullough equation. Journal of Applied Mathematics, 2013. https://doi.org/10.1155/2013/364718
• Xu, F. (2008). Application of Exp-function method to symmetric regularized long wave (SRLW) equation. Physics Letters A, 372(3), 252-257. https://doi.org/10.1016/j.physleta.2007.07.035