Yıl: 2023 Cilt: 13 Sayı: 1 Sayfa Aralığı: 123 - 129 Metin Dili: İngilizce DOI: 10.11121/ijocta.2023.1321 İndeks Tarihi: 12-07-2023

M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation

Öz:
This article aims to examine M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation (FE), which is a generalization of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations. The fractional (4+1)$-dimensional Fokas equation with the M-truncated derivatives is also studied first time in this study. The generalized projective Riccati equations method (GPREM) is successfully implemented. In the application of the presented method, a suitable fractional wave transformation is chosen to convert the proposed model into a nonlinear ordinary differential equation. Then, a linear equation system is acquired utilizing the GPREM, the system is solved, and the suitable solution sets are obtained. Dark and singular soliton solutions are successfully derived. Under the selection of appropriate values of the parameters, 2D, 3D, and contour plots are also displayed for some solutions.
Anahtar Kelime: (4+1)-dimensional Fokas equation M -truncated derivative Soliton solution

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Ozisik, M., Secer, A., & Bayram, M. (2022). Dispersive optical solitons of Biswas–Arshed equation with a couple of novel approaches. Optik, 265, 169547.
  • [2] Esen, H., Ozisik, M., Secer, A., & Bayram, M. (2022). Optical soliton perturbation with Fokas–Lenells equation via enhanced modi- fied extended tanh-expansion approach. Op- tik, 267, 169615.
  • [3] Ozisik, M., Bayram, M., Secer, A., Cinar, M., Yusuf, A., & Sulaiman, T. A. (2022). Opti- cal solitons to the (1+ 2)-dimensional Chiral non-linear Schr ̈odinger equation. Optical and Quantum Electronics, 54(9), 1-13.
  • [4] Yildirim, Y., Biswas, A., Alshehri, H. M., & Belic, M. R. (2022). Cubic–quartic optical soliton perturbation with Gerd- jikov–Ivanov equation by sine-Gordon equa- tion approach. Optoelectronics and Advanced Materials-Rapid Communications, 16(5-6), 236-242.
  • [5] Yildirim, Y., Biswas, A., & Alshehri, H. M. (2022). Cubic–quartic optical soliton pertur- bation with Fokas–Lenells equation having maximum intensity. Optik, 169336.
  • [6] Alquran, M. (2021). Physical properties for bidirectional wave solutions to a general- ized fifth-order equation with third-order time-dispersion term. Results in Physics, 28, 104577.
  • [7] Kocak, H. (2021). Kink and anti-kink wave solutions for the generalized KdV equation with Fisher-type nonlinearity. An Interna- tional Journal of Optimization and Control: Theories & Applications (IJOCTA), 11(2), 123-127.
  • [8] Hoque, M. F., & Roshid, H. O. (2020). Op- tical soliton solutions of the Biswas-Arshed model by the tan(⊖/2) expansion approach. Physica Scripta, 95, 075219.
  • [9] Al-Askar, F. M., Mohammed, W. W., Ce- sarano, C., & El-Morshedy, M. (2022). The influence of multiplicative noise and fractional derivative on the solutions of the stochastic fractional Hirota–Maccari system. Axioms, 11(8), 357.
  • [10] Yusuf, A., Inc, M., & Baleanu, D. (2019). Optical solitons with M-truncated and beta derivatives in nonlinear optics. Frontiers in Physics, 7, 126.
  • [11] Akram, G., Sadaf, M., & Zainab, I. (2022). Observations of fractional effects of β-derivative and M-truncated derivative for space time fractional Φ − 4 equation via two analytical techniques. Chaos, Solitons & Fractals, 154, 111645.
  • [12] Hashemi, M. S. (2018). Some new exact solu- tions of (2 + 1)-dimensional nonlinear Heisen- berg ferromagnetic spin chain with the con- formable time fractional derivative. Optical and Quantum Electronics, 50(2), 1-11.
  • [13] Cinar, M., Secer, A., & Bayram, M. (2022). Analytical solutions of (2 + 1)-dimensional Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics using the New Kudryashov method. Physica Scripta, 97(9), 094002.
  • [14] Esen, H., Secer, A., Ozisik, M., & Bayram, M. (2022). Dark, bright and singular optical solutions of the Kaup–Newell model with two analytical integration schemes. Optik, 261, 169110.
  • [15] Onder, I., Secer, A., Ozisik, M., & Bayram, M. (2022). On the optical soliton solutions of Kundu–Mukherjee–Naskar equation via two different analytical methods. Optik, 257, 168761.
  • [16] Akinyemi, L., S ̧enol, M., Az-Zo’bi, E., Veeresha, P., & Akpan, U. (2022). Novel soliton solutions of four sets of generalized (2+ 1)-dimensional Boussinesq–Kadomtsev–Petviashvili-like equations. Modern Physics Letters B, 36(01), 2150530.
  • [17] Akinyemi, L., Veeresha, P., Darvishi, M. T., Rezazadeh, H., S ̧enol, M., & Akpan, U. (2022). A novel approach to study generalized coupled cubic Schr ̈odinger- Korteweg-de Vries equations. Journal of Ocean Engineering and Science, DOI: https://doi.org/10.1016/j.joes.2022.06.004.
  • [18] Veeresha, P. (2022). Analysis of the spread of infectious diseases with the effects of con- sciousness programs by media using three fractional operators. In Methods of Mathe- matical Modelling (pp. 113-135). Academic Press.
  • [19] Yao, S. W., Ilhan, E., Veeresha, P., & Baskonus, H. M. (2021). A power- ful iterative approach for quintic com- plex Ginzburg–Landau equation within the frame of fractional operator. Fractals, 29(05), 2140023.
  • [20] Podlubny, I. (1999). Fractional Differential Equations. Academic Press, San Diego.
  • [21] Veeresha, P., Ilhan, E., & Baskonus, H. M. (2021). Fractional approach for analysis of the model describing wind-influenced projec- tile motion. Physica Scripta, 96(7), 075209.
  • [22] Atangana, A., & Koca, I. (2016). Chaos in a simple nonlinear system with Atan- gana–Baleanu derivatives with fractional or- der. Chaos, Solitons & Fractals, 89, 447-454.
  • [23] Baishya, C., & Veeresha, P. (2021). Laguerre polynomial-based operational matrix of inte- gration for solving fractional differential equa- tions with non-singular kernel. Proceedings of the Royal Society A, 477(2253), 20210438.
  • [24] Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of frac- tional derivative. Journal of Computational and Applied Mathematics, 264, 65-70.
  • [25] Fokas, A. S. (2006). Integrable nonlinear evo- lution partial differential equations in 4 + 2 and 3 + 1 dimensions. Physical review letters, 96(19), 190201.
  • [26] He, Y. (2014). Exact solutions for (4 + 1)- dimensional nonlinear Fokas equation using extended F-expansion method and its variant. Mathematical Problems in Engineering, 2014.
  • [27] Zhang, S., Tian, C., & Qian, W. Y. (2016). Bilinearization and new multisoliton solutions for the (4+1)-dimensional Fokas equation. Pramana, 86(6), 1259-1267.
  • [28] Kim, H., & Sakthivel, R. (2012). New ex- act traveling wave solutions of some nonlinear higher-dimensional physical models. Reports on Mathematical Physics, 70(1), 39-50.
  • [29] Ullah, N., Asjad, M. I., Awrejcewicz, J., Muhammad, T., & Baleanu, D. (2022). On soliton solutions of fractional-order nonlin- ear model appears in physical sciences. AIMS Mathematics, 7(5), 7421-7440.
  • [30] Xu, B., & Zhang, S. (2019). Exact solu- tions with arbitrary functions of the (4 + 1)-dimensional Fokas equation. Thermal Sci- ence, 23(4), 2403-2411.
  • [31] Wazwaz, A. M. (2021). A variety of multiple- soliton solutions for the integrable (4+1)- dimensional Fokas equation. Waves in Ran- dom and Complex Media, 31(1), 46-56.
  • [32] Al-Amr, M. O., & El-Ganaini, S. (2017). New exact traveling wave solutions of the (4 + 1)-dimensional Fokas equation. Comput- ers & Mathematics with Applications, 74(6), 1274-1287.
  • [33] Baskonus, H. M., Kumar, A., Kumar, A., & Gao, W. (2020). Deeper investigations of the (4 + 1)-dimensional Fokas and (2 + 1)- dimensional Breaking soliton equations. In- ternational Journal of Modern Physics B, 34(17), 2050152.
APA Ozdemir N (2023). M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. , 123 - 129. 10.11121/ijocta.2023.1321
Chicago Ozdemir Neslihan M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. (2023): 123 - 129. 10.11121/ijocta.2023.1321
MLA Ozdemir Neslihan M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. , 2023, ss.123 - 129. 10.11121/ijocta.2023.1321
AMA Ozdemir N M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. . 2023; 123 - 129. 10.11121/ijocta.2023.1321
Vancouver Ozdemir N M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. . 2023; 123 - 129. 10.11121/ijocta.2023.1321
IEEE Ozdemir N "M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation." , ss.123 - 129, 2023. 10.11121/ijocta.2023.1321
ISNAD Ozdemir, Neslihan. "M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation". (2023), 123-129. https://doi.org/10.11121/ijocta.2023.1321
APA Ozdemir N (2023). M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 13(1), 123 - 129. 10.11121/ijocta.2023.1321
Chicago Ozdemir Neslihan M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 13, no.1 (2023): 123 - 129. 10.11121/ijocta.2023.1321
MLA Ozdemir Neslihan M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), vol.13, no.1, 2023, ss.123 - 129. 10.11121/ijocta.2023.1321
AMA Ozdemir N M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. An International Journal of Optimization and Control: Theories & Applications (IJOCTA). 2023; 13(1): 123 - 129. 10.11121/ijocta.2023.1321
Vancouver Ozdemir N M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation. An International Journal of Optimization and Control: Theories & Applications (IJOCTA). 2023; 13(1): 123 - 129. 10.11121/ijocta.2023.1321
IEEE Ozdemir N "M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation." An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 13, ss.123 - 129, 2023. 10.11121/ijocta.2023.1321
ISNAD Ozdemir, Neslihan. "M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation". An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 13/1 (2023), 123-129. https://doi.org/10.11121/ijocta.2023.1321