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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2021 / Cilt: 21 - Sayı: 5

Construction of Soliton Solutions for Chaffee-Infante Equation

Chaffee-Infante Denklemi için Soliton Çözümlerinin Oluşturulması

Şeyma TULUCE DEMIRAY
Pages
1046–1051
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, has been studied on the Chaffee-Infante equation and soliton solutions of these equation are examined.
📊
Key Findings & Data:In accordance with this purpose, The sine-Gordon expansion method, which is one of the solution methods of nonlinear partial differential equations, was used.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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.

Özet

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.

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Cite This Article

DEMIRAY, Ş. T. (2022). Construction of Soliton Solutions for Chaffee-Infante Equation. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 21 - Sayı: 5, 1046–1051. https://ajindex.com/articles/429634

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References (12)

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Mao, Y., 2018. Exact solutions to (2 + 1)-dimensional Chaffee–Infante equation, Pramana-J. Physics, 91, 9, 1–4.
  11. 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.
  12. Sakthivel, R., Chun, C., 2010. New Soliton Solutions of Chaffee-Infante Equations Using the Exp-Function Method, Function Method, Ze