Deriving Novel wave solutions to the (2+1)-dimensional fractional Paraxial wave dynamical equation with Kerr law using the $({G}'/G^2) $-expansion function technique

E. Abd Elbary, Fatma; Semary, Mourad S.; Fareed, ِِAisha F.; Elsesy, Mohammed A.

doi:10.22034/cmde.2025.64296.2908

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	45
تعداد شماره‌ها	1,550
تعداد مقالات	18,890
تعداد مشاهده مقاله	63,334,379
تعداد دریافت فایل اصل مقاله	23,088,971

	Deriving Novel wave solutions to the (2+1)-dimensional fractional Paraxial wave dynamical equation with Kerr law using the $({G}'/G^2) $-expansion function technique
Computational Methods for Differential Equations
مقاله 27، دوره 14، شماره 3، مهر 2026، صفحه 1442-1457 اصل مقاله (6.78 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.64296.2908
نویسندگان
Fatma E. Abd Elbary¹؛ Mourad S. Semary²؛ ِِAisha F. Fareed^* ³؛ Mohammed A. Elsesy⁴
¹Faculty of Engineering, MTI university, Cario, Egypt.
²Basic Sciences Department, Faculty of Engineering, Badr University in Cairo, Cairo 11829, Egypt.
³Department of Electrical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Al Kharj 16278, Saudi Arabia.
⁴Department of Basic Engineering Sciences, Faculty of Engineering Benha, Benha university, Egypt.
چکیده
The method is used to find traveling wave solutions of nonlinear evolution equations (NLEEs), not "certain types". Specify "to find exact traveling wave solutions to certain types of nonlinear partial differential equations (NLPDEs)". In this case, the Paraxial Wave Dynamical Equation with Kerr law (PWDE) in the sense of the truncated $ \mathsf{M} $-fractional derivative. This equation is important in the study of wave propagation and optical phenomena. By employing this method, the researchers were able to obtain new, previously unknown exact solutions to this equation. These solutions represent different types of wave solutions, each with their own unique characteristics and properties. The significance of these novel wave solutions lies in their potential applications in physics and engineering. Wave phenomena play a crucial role in various fields, such as optics, photonics, and electromagnetics. The researchers indicate that these specific wave solutions have important practical applications in these domains. Moreover, we provide visual representations of the obtained solutions in the form of 3D, contour, and 2D plots. These graphical illustrations serve to demonstrate the feasibility and reliability of our proposed technique, showcasing its ability to capture the essential characteristics and behaviors of the solutions.
کلیدواژه‌ها
Fractional calculus؛ the truncated M-fractional derivative؛ Exact solutions؛ (G′/G2)-expansion function method؛ Paraxial Wave Dynamical Equation (PWDE)

مراجع
[1] K. K. Ali, F. E. Abd Elbary, M. S. Abdel-Wahed, M. A. Elsisy, and M. S. Semary, Solitary Wave Solution for Fractional-Order General Equal-Width Equation via Semi Analytical Technique, Appl. Math., 17(3) (2023), 483–493. [2] K. K. Ali and M. Maneea, New approximation solution for time-fractional Kudryashov-Sinelshchikov equation using novel technique, Alex. Eng. J., 72 (2023), 559–572. [3] K. K. Ali, F. E. Abd Elbary, M. S. Abdel-Wahed, M. A. Elsisy, and M. S. Semary, Solving Nonlinear Fractional PDEs with Applications to Physics and Engineering Using the Laplace Residual Power Series Method, Int. J. Differ. Equ., 1 (2023), 1240970. [4] A. Atangana, Exact solution of the time-fractional ground water flow equation within a leaky aquifer equation, J. Vibration Control, 22(7) (2016), 1749–1756. [5] M. Arshad, A. R. Seadawy, D. Lu, and F. U. Khan, Optical solitons of the paraxial wave dynamical model in Kerr media and its applications in nonlinear optics, Int. J. Mod. Phys., 34(9) (2020), 2050078. [6] M. Arshad, A. R. Seadawy, D. Lu, and M. S. Saleem, Elliptic function solutions, modulation instability and optical solitons analysis of the paraxial wave dynamical model with Kerr media, Opt. Quantum Electron., 53 (2021), 1–20. [7] M. H. Bashar, S. Ghosh, and M. M. Rahman, Dynamical exploration of optical soliton solutions for M-fractional Paraxial wave equation, Plos One, 19(2) (2024), 299573. [8] S. Behera, N. Aljahdaly, and J. Virdi, On the modified (G′/G2)-expansion method for finding some analytical solutions of the traveling waves, J. Ocean Eng. Sci., 7(4) (2022), 313–320. [9] X. Y. Gao, Y. J. Guo, and W. R. Shan, Symbolically computing the shallow water via a (2+1)-dimensional gener- alized modified dispersive water-wave system: Similarity reductions, scaling and hetero-Bäcklund transformations, Qual. Theory Dyn. Syst., 22(1) (2023), 17. [10] W. Hamali, J. Manafian, M. Lakestani, A. M. Mahnashi, and A. Bekir, Optical solitons of M-fractional nonlinear Schrödinger’s complex hyperbolic model by generalized Kudryashov method, Opt. Quantum Electron., 56(1) (2024), 7 [11] Z. Z. Kang and T. C. Xia, Construction of abundant solutions of the (2+1)-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation, Appl. Math. Lett., 103 (2020), 106163. [12] Z. Z. Kang and R. C. Yang, On multi-soliton solutions to a generalized inhomogeneous nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin chain, Nonlinear Dyn., 110(4) (2022), 3605–3615. [13] M. M. Khater, A. M. Alabdali, A. Mashat, and S. A. Salama, Optical soliton wave solutions of the fractional complex paraxial wave dynamical model along with Kerr media, Fractals, 30(5) (2022), 2240153. [14] M. Lakestani and J. Manafian, Analytical treatments of the space-time fractional coupled nonlinear Schr¨odinger equations, Opt. Quantum Electron., 50 (2018), 1–33. [15] P. Malingam, P. Wongsasinchai, S. Sirisubtawee, and S. Koonprasert, Exact Solutions of the Paraxial Wave Dy- namical Model in Kerr Media with Truncated M-fractional Derivative using the (G’/G, 1/G)-Expansion Method, WSEAS Trans. Syst. Control, 18 (2023), 498–512. [16] J. Manafian and M. Lakestani, Interaction among a lump, periodic waves, and kink solutions to the fractional generalized CBS–BK equation, Math. Methods Appl. Sci., 44(1) (2021), 1052–1070. [17] Y. Meng, Expanded (G′/G2)-expansion method to solve separated variables for the (2+1)-dimensional NNV equation, Adv. Math. Phys., 2018 (2018), 9248174. [18] S. K. Mohanty, O. V. Kravchenko, M. K. Deka, A. N. Dev, and D. V. Churikov, The exact solutions of the (2+1)- dimensional Kadomtsev–Petviashvili equation with variable coefficients by extended generalized (G′/G)-expansion method, J. King Saud Univ. Sci., 35(1) (2023), 102358. [19] S. T. Mohyud-Din and S. Bibi, Exact solutions for nonlinear fractional differential equations using (G′/G2)- expansion method, Alex. Eng. J., 57 (2018), 1003–1008. [20] H. U. Rehman, A. U. Awan, S. A. Allahyani, E. M. Tag-ElDin, M. A. Binyamin, and S. Yasin, Exact solution of paraxial wave dynamical model with Kerr Media by using ϕ6 model expansion technique, Results Phys., 42 (2022), 105975. [21] H. U. Rehman, A. R. Seadawy, M. Younis, S. Yasin, S. T. Raza, and S. Althobaiti, Monochromatic optical beam propagation of paraxial dynamical model with Kerr media, Results Phys., 31 (2021), 105015. [22] M. Sadaf, S. Arshed, and G. Akram, Exact soliton and solitary wave solutions to the Fokas system using two variables (G′/G, 1/G)-expansion technique and generalized projective Riccati equation method, Optik, 268 (2022), 169713. [23] S. Sirisubtawee, S. Koonprasert, and S. Sungnul, New exact solutions of the conformable space-time Sharma–Tasso–Olver equation using two reliable methods, Symmetry, 12 (2020), 644. [24] J. Sousa and E. C. de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, arXiv preprint arXiv:1704.08187 (2017). [25] J. V. D. A. C. Sousa, E. Capelas, and D. E. Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Int. J. Anal. Appl., 16 (2018), 83–96. [26] T. A. Sulaiman, G. Yel, and H. Bulut, M-fractional solitons and periodic wave solutions to the Hirota–Maccari system, Mod. Phys. Lett. B, 33 (2019), 1950052. [27] N. Ullah, Exact solutions of paraxial wave dynamical model with Kerr law non-linearity using analytical techniques, Open J. Math. Sci., 7(1) (2023), 172–179. [28] P. Weinberger, John Kerr and his effects found in 1877 and 1878, Philos. Mag. Lett., 88(12) (2008), 897–907. [29] S. W. Yao, R. Manzoor, A. Zafar, M. Inc, S. Abbagari, and A. Houwe, Exact soliton solutions to the Cahn–Allen equation and predator–prey model with truncated M-fractional derivative, Results Phys., 37 (2022), 105455. [30] F. Yihu and L. Hou, The solitary wave solution for Quantum plasma Nonlinear dynamic model, Adv. Math. Phys., 2020(1) (2020), 5602373. [31] I. Zainab and G. Akram, Effect of β-derivative on time fractional Jaulent-Miodek system under modified auxiliary equation method and exp(-g(Ω))-expansion method, Chaos, Solitons Fractals, 168 (2023), 113147. [32] K. Zhouzheng, (G′/G2)-expansion Solutions to MBBM and OBBM Equations, J. Part. Differ. Equ., 28 (2015), 158–166.
آمار تعداد مشاهده مقاله: 379 تعداد دریافت فایل اصل مقاله: 626

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Deriving Novel wave solutions to the (2+1)-dimensional fractional Paraxial wave dynamical equation with Kerr law using the $({G}'/G^2) $-expansion function technique