Refraction simulation of nonlinear wave for Shallow Water-Like equation

Öz

The generalized (3+1) dimensional Shallow Water-Like equation (SWL), which is one of the higher dimensional evolution equations, is successfully constructed by aid of the (1/G')-expansion method, which is one of the analytical solution instruments in mathematics. Solitary waves are depicted by assigning specific values to the parameters in the SWL equation travelling wave solutions, which has an important place in physically energy transport. Graphics representing the solitary wave at any given moment are displayed in 2D, 3D and contours. A simulation of the wave is created for different values of velocity of solitary wave, which is a physical quantity. In addition, by keeping the parameters other than the rupture event of the wave constant, the situation at which speed the wave reaches to the breakage event is discussed.

Anahtar Kelimeler

• Exact solution
• (1/G')-expansion method
• solitary wave.

Kaynakça

1. [1]. Yavuz, M, Yokus, A. 2020. Analytical and numerical approaches to nerve impulse model of fractional‐order, Numerical Methods for Partial Differential Equations; 36(6): 1348-1368.
2. [2]. Yokus, A, Yavuz, M. 2020. Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation. Discrete & Continuous Dynamical Systems-S; doi, 10.
3. [3]. Benetazzo, A, Barbariol, F, Pezzutto, P, Staneva, J, Behrens, A, Davison, S, Cavaleri, L. 2021. Towards a unified framework for extreme sea waves from spectral models: Rationale and applications, Ocean Engineering; 219: 108263.
4. [4]. 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.
5. [5]. Raissi, M, Karniadakis, G, E. 2018. Hidden physics models: Machine learning of nonlinear partial differential equations. Journal of Computational Physics; 357: 125-141.
6. [6]. Duran, S. 2020. Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G'/G, 1/G)-Expansion Method. Adıyaman Üniversitesi Fen Bilimleri Dergisi; 10(2): 585-594.
7. [7]. Yokuş, A. 2018. Comparison of Caputo and conformable derivatives for time-fractional Korteweg–de Vries equation via the finite difference method. International Journal of Modern Physics B; 32(29): 1850365.
8. [8]. Russell, J. S. Report on Waves; Made to the Meetings of the British Association in 1845; pp 1842-43.

9. [9]. Duran, S, Yokuş, A, Durur, H, Kaya, D. 2021. Refraction simulation of internal solitary waves for the fractional Benjamin–Ono equation in fluid dynamics. Modern Physics Letters B; 35(26): 2150363.
10. [10]. Saleh, R, Mabrouk, S. M, Wazwaz, A, M. 2021. Lie symmetry analysis of a stochastic gene evolution in double-chain deoxyribonucleic acid system. Waves in Random and Complex Media; 1-15.
11. [11]. Ali, K, K, Seadawy, A, R, Yokus, A, Yilmazer, R, Bulut, H. 2020. Propagation of dispersive wave solutions for (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov equation in plasma physics. International Journal of Modern Physics B; 34(25): 2050227.
12. [12]. Nestor, S, Houwe, A, Rezazadeh, H, Betchewe, G, Bekir, A, Doka, S, Y. 2021. Chirped W-shape bright, dark and other solitons solutions of a conformable fractional nonlinear Schrödinger’s equation in nonlinear optics. Indian Journal of Physics; 1-13.
13. [13]. Feng, Z. 2002. The first-integral method to study the Burgers–Korteweg–de Vries equation. Journal of Physics A: Mathematical and General; 35(2): 343.
14. [14]. Yokus, A, Durur, H, Ahmad, H, Yao, S, W. 2020. Construction of different types analytic solutions for the Zhiber-Shabat equation. Mathematics; 8(6): 908.
15. [15]. Silambarasan, R, Kilicman, A. 2021. Solitons of nonlinear dispersive wave steered from Navier-Bernoulli hypothesis and Love's hypothesis in the cylindrical elastic rod with compressible Murnaghan's materials. arXiv preprint arXiv:2101.05070.
16. [16]. Kumar, S, Kumar, A, Wazwaz, A, M. 2020. New exact solitary wave solutions of the strain wave equation in microstructured solids via the generalized exponential rational function method. The European Physical Journal Plus; 135(11): 1-17.
17. [17]. Park, C, Khater, M, M, Abdel-Aty, A, H, Attia, R, A, Rezazadeh, H, Zidan, A, M, Mohamed, A, B. 2020. Dynamical analysis of the nonlinear complex fractional emerging telecommunication model with higher–order dispersive cubic–quintic. Alexandria Engineering Journal; 59(3): 1425-1433.
18. [18]. Duran, S. 2021. Travelling wave solutions and simulation of the Lonngren wave equation for tunnel diode. Optical and Quantum Electronics; 53(8): 1-9.
19. [19]. Yokuş, A, Durur, H, Abro, K, A, Kaya, D. 2020. Role of Gilson–Pickering equation for the different types of soliton solutions: a nonlinear analysis. The European Physical Journal Plus; 135(8): 1-19.
20. [20]. Li, Z, Manafian, J, Ibrahimov, N, Hajar, A, Nisar, K. S, Jamshed, W. 2021. Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis. Results in Physics; 28: 104490.
21. [21]. Zhang, Z, Li, B, Chen, J, Guo, Q. 2021. Construction of higher-order smooth positons and breather positons via Hirota’s bilinear method. Nonlinear Dynamics; 105(3): 2611-2618.
22. [22]. Wang, K, J, Liu, J, H. 2022. On abundant wave structures of the unsteady korteweg-de vries equation arising in shallow water. Journal of Ocean Engineering and Science.
23. [23]. Seadawy, A, R, Rehman, S, U, Younis, M, Rizvi, S, T, R, Althobaiti, S, Makhlouf, M, M. 2021. Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer-Chree equation. Physica Scripta; 96(4): 045202.
24. [24]. Alotaibi, M, F, Omri, M, Khalil, E, M, Abdel-Khalek, S, Bouslimi, J, Khater, M, M. 2022. Abundant solitary and semi-analytical wave solutions of nonlinear shallow water wave regime model. Journal of Ocean Engineering and Science.
25. [25]. Yilmaz, E, U, Khodad, F, S, Ozkan, Y, S, Abazari, R, Abouelregal, A, E, Shaayesteh, M, T, ... Ahmad, H. 2022. Manakov model of coupled NLS equation and its optical soliton solutions. Journal of Ocean Engineering and Science.
26. [26]. Yokus, A. 2020. On the exact and numerical solutions to the FitzHugh–Nagumo equation. International Journal of Modern Physics B; 34(17): 2050149.
27. [27]. Özkan, Y, S, Eslami, M, Rezazadeh, H. 2021. Pure cubic optical solitons with improved $$ tan (\varphi/2) $$ tan (φ/2)-expansion method. Optical and Quantum Electronics; 53(10): 1-13.
28. [28]. Baskonus, H, M, Eskitascioglu, E, I. 2020. Complex wave surfaces to the extended shallow water wave model with (2+1)-dimensional. Computational Methods for Differential Equations; 8(3): 585-596.
29. [29]. Zayed, E, M, E. 2010. Traveling wave solutions for higher dimensional nonlinear evolution equations using the G’/G-expansion method, Journal of Applied Mathematics & Informatics; 28(1_2): 383-395.
30. [30]. Zhang, Y, Dong, H, Zhang, X, Yang, H. 2017. Rational solutions and lump solutions to the generalized (3+1)-dimensional shallow water-like equation, Computers & Mathematics with Application; 73(2): 246-252.
31. [31]. Dusunceli, F. 2019. Exact Solutions for Generalized (3+1)-Dimensional Shallow Water-Like (SWL) Equation, In Conference Proceedings of Science and Technology; 2(1): 55-57.
32. [32]. Durur, H, Yokuş, A. 2020. Analytical solutions of Kolmogorov–Petrovskii–Piskunov equation. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi; 22(2): 628-636.
33. [33]. Yokus, A, Durur, H, Ahmad, H. 2020. Hyperbolic type solutions for the couple Boiti-Leon-Pempinelli system. Facta Universitatis, Series: Mathematics and Informatics; 35(2): 523-531.