Düzenli Uzun Dalga Denkleminin Hiperbolik Tip Yürüyen Dalga Çözümleri

Yıl 2020, Cilt: 7 Sayı: 2, 815 - 824, 30.12.2020

Hülya Durur , Asıf Yokuş , Doğan Kaya

https://doi.org/10.35193/bseufbd.698820

Cited By: 5

Öz

Bu çalışmanın genel amacı (1/G') -açılım yöntemi kullanılarak Düzenli Uzun Dalga (RWL) denklemi için yürüyen dalga çözümlerini elde etmektir Elde Edilen çözümlerde sabitlere özel değerler verilerek 3 boyutlu, 2 boyutlu ve kontur grafikleri sunulmuştur. Bu grafikler Düzenli Uzun Dalga denkleminin özel bir çözümüdür ve denklemin durağan bir dalgasını temsil etmektedir. Bu makalede sunulan çözümleri ve grafikleri bulmak için bilgisayar paket programı kullanılmaktadır.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        

Anahtar Kelimeler

(1/G') -Açılım Yöntemi, Düzenli Uzun Dalga Denklemi, Yürüyen Dalga Çözümü, Tam Çözüm

Hyperbolic Type Traveling Wave Solutions of Regularized Long Wave Equation

Öz

The main goal of this study is to obtain the traveling wave solutions for Regularized Long Wave (RLW) equation by using (1/G') -expansion method. By giving special values to the constants in the solutions obtained, 3D, 2D, and contour graphics are presented. These graphics are a special solution of the (RLW) equation, and they represent a stationary wave of the equation. A computer package program is used to find the solutions and graphics presented in this article.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       

Anahtar Kelimeler

(1/G') -Expansion Method, Regularized Long Wave Equation, Traveling Wave Solution, Exact Solution

Kaynakça

• Silambarasan, R., Baskonus, H. M., & Bulut, H. (2019). Jacobi elliptic function solutions of the double dispersive equation in the Murnaghan's rod. The European Physical Journal Plus, 134(3), 125.
• Faraj, B., & Modanli, M. (2017). Using difference scheme method for the numerical solution of telegraph partial differential equation. Journal of Garmian University, 3, 157-163.
• Yokus, A., & Yavuz, M. (2018). Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation. Discrete & Continuous Dynamical Systems-S, 0.
• Yokuş, A., & Durur, H. (2019). Complex hyperbolic traveling wave solutions of Kuramoto-Sivashinsky equation using (1/G') expansion method for nonlinear dynamic theory. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21(2), 590-599.
• Durur H., & Yokuş, A. (1/G')-Açılım Metodunu Kullanarak Sawada–Kotera Denkleminin Hiperbolik Yürüyen Dalga Çözümleri. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi. 2019; 19(3): 615-619.
• Durur, H., Şenol, M., Kurt, A., & Taşbozan, O. Zaman-Kesirli Kadomtsev-Petviashvili Denkleminin Conformable Türev ile Yaklaşık Çözümleri. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12(2), 796-806.
• Prakasha, D. G., Veeresha, P., & Baskonus, H. M. (2019). Residual power series method for fractional Swift–Hohenberg equation. Fractal and Fractional, 3(1), 9.
• 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.
• Sulaiman, T. A., Bulut, H., Yokus, A., & Baskonus, H. M. (2019). On the exact and numerical solutions to the coupled Boussinesq equation arising in ocean engineering. Indian Journal of Physics, 93(5), 647-656.
• Yokus, A., Baskonus, H. M., Sulaiman, T. A., & Bulut, H. (2018). Numerical simulation and solutions of the two‐component second order KdV evolutionarysystem. Numerical Methods for Partial Differential Equations, 34(1), 211-227.
• Durur, H. (2019). Different types analytic solutions of the (1+ 1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method. Modern Physics Letters B, 2050036.
• Khan, H., Barak, S., Kumam, P., & Arif, M. (2019). Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method. Symmetry, 11(4), 566.
• Kaya, D., & Yokus, A. (2005). A decomposition method for finding solitary and periodic solutions for a coupled higher-dimensional Burgers equations. Applied Mathematics and Computation, 164(3), 857-864.
• Aziz, I., & Šarler, B. (2010). The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets. Mathematical and Computer Modelling, 52(9-10), 1577-1590.
• Aziz, I., & Asif, M. (2017). Haar wavelet collocation method for three-dimensional elliptic partial differential equations. Computers & Mathematics with Applications, 73(9), 2023-2034.
• Durur, H., Kurt, A., & Tasbozan, O. (2020). New Travelling Wave Solutions for KdV6 Equation Using Sub Equation Method. Applied Mathematics and Nonlinear Sciences, 5(1), 455-460.
• Durur, H., Taşbozan, O., Kurt, A., & Şenol, M. New Wave Solutions of Time Fractional Kadomtsev-Petviashvili Equation Arising In the Evolution of Nonlinear Long Waves of Small Amplitude. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12(2), 807-815.
• Yavuz, M., & Ozdemir, N. (2018). Numerical inverse Laplace homotopy technique for fractional heat equations. Thermal Science, 22(Suppl. 1), 185-194.
• Kurt, A., Tasbozan, O., and Durur, H., The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method. Fundamental Journal of Mathematics and Applications, 2(2), 173-179, (2019).
• Kabir, M. M., Borhanifar, A., & Abazari, R. (2011). Application of (G′ G)-expansion method to Regularized Long Wave (RLW) equation. Computers & Mathematics with Applications, 61(8), 2044-2047. Kaya, D. (2004). A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation. Applied Mathematics and Computation, 149(3), 833-841.
• Soliman, A. A. (2005). Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method. Mathematics and Computers in Simulation, 70(2), 119-124.
• Esen, A., & Kutluay, S. (2006). Application of a lumped Galerkin method to the regularized long wave equation. Applied Mathematics and Computation, 174(2), 833-845.
• El-Danaf, T. S., Ramadan, M. A., & Alaal, F. E. A. (2005). The use of adomian decomposition method for solving the regularized long-wave equation. Chaos, Solitons & Fractals, 26(3), 747-757.
• Kutluay, S., & Esen, A. (2006). A finite difference solution of the regularized long-wave equation. Mathematical Problems in Engineering, 2006.
• Daǧ, İ. (2000). Least-squares quadratic B-spline finite element method for the regularised long wave equation. Computer Methods in Applied Mechanics and Engineering, 182(1-2), 205-215.
• Dehghan, M., & Salehi, R. (2011). The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas. Computer Physics Communications, 182(12), 2540-2549.
• Ahmad, H., Khan, T. A., Durur, H., Ismail, G. M., & Yokus, A. (2020). Analytic approximate solutions of diffusion equations arising in oil pollution. Journal of Ocean Engineering and Science.
• Yokus, A. (2020). On the exact and numerical solutions to the FitzHugh–Nagumo equation. International Journal of Modern Physics B, 2050149.
• 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.
• 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.
• Durur, H., & Yokuş, A. (2020). Analytical solutions of Kolmogorov–Petrovskii–Piskunov equation. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(2), 628-636.
• Yokus, A., Kuzu, B., & Demiroğlu, U. (2019). Investigation of solitary wave solutions for the (3+ 1)-dimensional Zakharov–Kuznetsov equation. International Journal of Modern Physics B, 33(29), 1950350.
• Modanli, M. (2019). On the numerical solution for third order fractional partial differential equation by difference scheme method. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 9(3), 1-5.
• Yavuz, M. (2017). Novel solution methods for initial boundary value problems of fractional order with conformable differentiation. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 8(1), 1-7.