Construction of Soliton Solutions for Chaffee-Infante Equation

Year 2021, , 1046 - 1051, 31.10.2021

Şeyma Tülüce Demiray , Uğur Bayrakcı

https://doi.org/10.35414/akufemubid.946217

Cited By: 5

Abstract

In this article, has been studied on the Chaffee-Infante equation and soliton solutions of these equation are examined. In accordance with this purpose, The sine-Gordon expansion method, which is one of the solution methods of nonlinear partial differential equations, was used. Also graphical representation of the obtained results of the specified equation is made using Wolfram Mathematica 12 for certain values and thus the conformity of the founded results has been demonstrated.

Keywords

Chafee-Infante equation, Sine-Gordon expansion method, Soliton solutions, Exact solutions

Chaffee-Infante Denklemi için Soliton Çözümlerinin Oluşturulması

Abstract

Bu makalede, Chaffee-Infante denklemi üzerinde çalışılmıştır ve bu denklemin soliton çözümleri incelenmiştir. Bu amaç doğrultusunda, lineer olmayan kısmi diferansiyel denklemlerin çözüm yöntemlerinden biri olan sine-Gordon açılım yöntemi kullanılmıştır. Ayrıca belirtilen denklemin elde edilen sonuçlarının grafiksel gösterimi belli değerler için Wolfram Mathematica 12 programı kullanılarak yapılmış ve böylece bulunan sonuçların uygunluğu gösterilmiştir.

Keywords

Chaffee-Infante Denklemi, Sine-Gordon açılım metodu, Soliton çözümler, Tam çözümler

References

• Akbar, M.A., Ali, N.H.M, Hussain, J., 2019. Optical soliton solutions to the (2 + 1)-dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation, Advances in Difference Equations, 2019, 1, 1–18.
• Akram, G., Mahak, N., 2018. Aplication of the first integral method for solving (1+1) dimensional cubic-quintic complex Ginzburg-Landau equation, Optik, 164, 210–217.
• Alam, M.N., Akbar, M.A., 2014. Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method, Journal of the Egyptian Mathematical Society, 22, 3, 402–406.
• Bulut, H., Sulaiman, T.A., Baskonus, H.M., 2016. New solitary and optical wave structures to the Korteweg–de Vries equation with dual-power law nonlinearity, Opt Quant Electron, 48, 564, 1–14.
• Duran, S., 2021. Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics, International Journal of Modern Physics B, 35, 9, 2150130.
• Durur, H., Tasbozan, O., Kurt, A., 2020. New Analytical Solutions of Conformable Time Fractional Bad and Good Modified Boussinesq Equations, Applied Mathematics and Nonlinear Sciences, 5, 1, 447–454.
• Durur, H., Yokuş, A., 2021. Discussions on difraction and the dispersion for traveling wave solutions of the (2+1)‑dimensional paraxial wave equation, Mathematical Sciences, 1–11.
• Habiba, U., Salam, M. A., Hossain, M. B., Datta, M., 2019. Solitary Wave Solutions of Chafee-Infante Equation and (2+1)-Dimensional Breaking Soliton Equation by the Improved Kudryashov Method, Global Journal of Science Frontier Research, 19, 5, 1–9.
• İlhan, O.A., Bulut, H., Sulaiman, T.A., Baskonus, H.M., 2020. On the new wave behavior of the Magneto-Electro-Elastic(MEE) circular rod longitudinal wave equation, An International Journal of Optimization and Control: Theories & Applications, 10, 1, 1–8.
• Kumar, D., Hosseini, K., Samadani, F., 2017. The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics, Optik, 149, 439–446.
• Mao, Y., 2018. Exact solutions to (2 + 1)-dimensional Chaffee–Infante equation, Pramana-J. Physics, 91, 9, 1–4.
• Qawasmeh, A., Alquran, M., 2014. Reliable Study of Some New Fifth-Order Nonlinear Equations by Means of G′/G Expansion Method and Rational Sine-Cosine Method, Applied Mathematical Sciences, 8, 120, 5985–5994.
• Sakthivel, R., Chun, C., 2010. New Soliton Solutions of Chaffee-Infante Equations Using the Exp-Function Method, Function Method, Zeitschrift für Naturforschung A, 65, 3, 197–202.
• Taghizadeh, N., Mirzazadeh, M., Paghaleh, A.S., 2012. Exact travelling wave solutions of Joseph-Egri(TRLW) equation by the extended homogeneous balance method, International Journal of Applied Mathematics and Computation, 4, 1, 96 – 104.
• Tahir, M., Kumar, S., Rehman, H., Ramzan, M., Hasan, A., Osman, M.S., 2020. Exact traveling wave solutions of Chaffee–Infante equation in (2 + 1)-dimensions and dimensionless Zakharov equation, Mathematical Methods in the Applied Sciences, 44, 2, 1500–1513.
• Tasbozan, O., Cenesiz, Y., Kurt, A., 2016. New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method, The European Physical Journal Plus, 131, 244, 1–14.
• Tuluce Demiray, S., Bulut, H., Onargan, G., 2015., An application of generalized tanh function method for the sixth-order Boussinesq (sB) equation and (1+1) dimensional dispersive long wave equation, Applied Mathematical Sciences, 9, 16, 773–790.
• Tuluce Demiray, S., Bulut, H., 2017a. Analytical solutions of Phi-four equation, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7, 3, 275-280.
• Tuluce Demiray, S., Bulut, H., 2017b. New exact solutions for generalized Gardner equation, Kuwait J. Sci., 44, 1, 1–8.
• Tuluce Demiray, S., Bulut, H., 2019. Soliton solutions of some non-linear evolution problems by GKM, Neural Computing and Applications, 31, 287–294.
• Wazwaz, A.M., 2005. The tanh method for generalized forms of nonlinear heat conduction and Burgers–Fisher equations, Applied Mathematics and Computation, 169, 1, 321-338.
• Yan, Z., Zhang, H., 1999. New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics, Physics Letters A, 252, 6, 291–296.
• Yokuş, A., Durur, H., Abro, K.A., 2021. Symbolic computation of Caudrey–Dodd–Gibbon equation subject to periodic trigonometric and hyperbolic symmetries, European Physical Journal Plus, 136, 4, 1–16.