On Travelling Wave Solutions of Dullin-Gottwald-Holm Dynamical Equation and Strain Wave Equation

Yıl 2022, Cilt: 11 Sayı: 3, 134 - 149, 29.09.2022

Şeyma Tülüce Demiray , Merve Davarcı Yalçın

https://doi.org/10.46810/tdfd.1099472

Öz

In this study, extended trial equation method (ETEM) is implemented to obtain exact solutions of the Dullin-Gottwald-Holm Dynamical equation (DGHDE) and the strain wave equation. We constitute some exact solutions such as soliton solutions, rational, Jacobi elliptic, periodic wave solutions and hyperbolic function solutions of these equations via ETEM. Then, we present results that we obtained by using this method.

Anahtar Kelimeler

The Dullin-Gottwald-Holm Dynamical equation, The strain wave equation, Extended trial equation method, Soliton solutions, Rational Jacobi elliptic and hyperbolic function solutions

Kaynakça

• [1] Wazwaz AM. The Hirota’s direct method and the tanh–coth method for multiplesoliton solutions of the Sawada–Kotera–Ito seventh-order equation, Applied Mathematics and Computation. 2008;199:133–8.
• [2] Pelap F, Kamga J, Fomethe A, Kenfack A, Faye M. Wave dynamics in a modified quintic complex Ginzburg-Landau system. Phys. Lett. A. 2009;373:1015-8.
• [3] Pandir Y, Ekin A. Dynamics of combined soliton solutions of unstable nonlinear Schrodinger equation with new version of the trial equation method. Chinese Journal of Physics. 2020;67:534-43.
• [4] Rizvi STR, Ali K, Sardar A, Younis M, Bekir A. Symbolic computation and abundant travelling wave solutions to KdV-mKdV equation. Pramana. 2017;88(16):1-6.
• [5] Irshad A, Mohyud-Din ST. Tanh-Coth Method for Nonlinear Differantial Equations. Studies in Nonlinear Sciences, 2012;3(1):24-48.
• [6] Pandir Y, Gurefe Y, Kadak U, Misirli E. Classification of exact solutions for some nonlinear partial differential equations with generalized evolution. Abstract and Applied Analysis. 2012;2012:1-16.
• [7] Bulut H, Pandir Y. Tuluce Demiray S. Exact Solutions of Nonlinear Schrodinger's Equation with Dual Power-Law Nonlinearity by Extended Trial Equation Method. Waves in Random and Complex Media. 2014;24(4):439-51.
• [8] Younas U, Seadawy AR, Younis M, Rizvi STR. Dispersive of propagation wave structures to the dullin-GottwaldHolm dynamical equation in a shallow water waves. Chinese Journal of Physics. 2020;68:348-64.
• [9] Octavian GM. Global conservative solutions of the Dullin-Gotwald-Holm Equation. Dıscrete and contınuous. 2007;19(3):575-94.
• [10] Raddadi MH, Younis M, Seadawy AR, Rehman SU, Bilal M, Rizvi STR, Althobaiti A. Dynamical behaviour of shallow water waves and solitary wave solutions of the Dullin-Gottwald-Holm dynamical system. Journal of King Saud University-Science. 2021;33(101627):1-9.
• [11] Gupta RK, Anupma B. The Dullin-Gottwald-Holm Equation: Classical Lie Approach and Exact Solutions. International Journal of Nonlinear Science. 2010;2(10):146-52.
• [12] Ayati Z, Hosseini K, Mirzazadeh M. Application of Kudryashov and functional variable methods to the strain wave equation in microstructured solids. Nonlinear Engineering. 2017;6(1):25–9.
• [13] Kumar S, Kumar A, Wazwaz AM. 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. 2020;135(870):1-17.
• [14] Hafez MG, Akbar MA. An exponential expansion method and its application to the strain wave equation in microstructured solids. Ain Shams Engineering Journal. 2015;6:683-90.