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Modification of Coupled Drinfel’d-Sokolov-Wilson Equation and Approximate Solutions by Optimal Perturbation Iteration Method

Year 2020, Volume: 20 Issue: 1, 35 - 40, 17.03.2020
https://doi.org/10.35414/akufemubid.649745

Abstract

References

  • Aktürk, T., Gürefe, Y., Pandır, Y., 2017. An application of the new function method to the Zhiber–Shabat equation, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7(3), 271-274.
  • Bildik, N., Deniz, S., 2017. A new efficient method for solving delay differential equations and a comparison with other methods, The European Physical Journal Plus, 132(1), 51.
  • Bildik, N., Deniz, S., 2018. New analytic approximate solutions to the generalized regularized long wave equations, Bulletin of the Korean Mathematical Society, 55(3), 749-762.
  • Bildik, N., Deniz, S., 2018. Solving the burgers' and regularized long wave equations using the new perturbation iteration technique, Numerical Methods for Partial Differential Equations, 34(5), 1489-1501.
  • Bulut, H., Baskonus, H. M., Pandir, Y., 2013. The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation. In Abstract and Applied Analysis (Vol. 2013). Hindawi.
  • Demiray, S. T., Pandir, Y., Bulut, H., 2016. All exact travelling wave solutions of Hirota equation and Hirota–Maccari system, Optik-International Journal for Light and Electron Optics, 127(4), 1848-1859.
  • Deniz, S., Bildik, N. 2018. Optimal perturbation iteration method for Bratu-type problems, Journal of King Saud University-Science, 30(1), 91-99.
  • Deniz, S. 2017. Optimal perturbation iteration method for solving nonlinear heat transfer equations. Journal of Heat Transfer, 139(7), 074503.
  • Fan, Engui, and Hongqing Zhang., 1998. A note on the homogeneous balance method. Physics Letters A 246(5), 403-406.
  • İnan, İ.E., 2019. Auto-Bäcklund Transformation for Fifth Order Equation of the Burgers Hierarchy, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 19, 021301, 328-334.
  • Inc, M., 2008. The approximate and exact solutions of the space-and time fractional Burgers’ equations with initial conditions by variational iteration method, Journal of Mathematical Analysis and Applications, 345(1), 476-484.
  • Guo, Boling, Liming Ling, and Q. P. Liu., 2012. Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions, Physical Review E, 85(2), 026607.
  • Manafian H.J. and Lakestani M.,2013. Solitary wave and periodic wave solutions for variants of the KdV-Burger and the K(n,n)-Burger equations by the generalized tanh-coth method, Communations in Numerical Analysis, 1–18.
  • Manafian H.J. and Zamanpour I.,2013. Analytical treatment of the coupled Higgs equation and the Maccari system via Exp-function method, Acta Universitatis Apulensis, 33, 203–216.
  • Matveev V.B. and Salle M.A., 1991. Darboux Transformations and Solitons, Springer, Berlin.
  • Malfliet W., 1992. Solitary wave solutions of nonlinear wave equations, American Journal of Physics, 60, 650-654.
  • Shang Y., 2007 Backlund transformation, Lax pairs and explicit exact solutions for the shallow water waves equation. Applied Mathematics and Computation, 187, 1286-1297.
  • Shen S. and Pan Z.,2003. A note on the Jacobi elliptic function expansion method, Physics Letters A, 308, 143-148.
  • Wadati, M., Heiji S., and Kimiaki K., 1975. Relationships among inverse method, Bäcklund transformation and an infinite number of conservation laws. Progress of theoretical physics 53(2) , 419-436.
  • Wazwaz, A.M., 2007. Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method. Applied Mathematics and Computation, 190(1), 633-640.

İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu

Year 2020, Volume: 20 Issue: 1, 35 - 40, 17.03.2020
https://doi.org/10.35414/akufemubid.649745

Abstract

Bu araştırma makalesinde, kısmi diferansiyel denklemler sistemi için yeni geliştirilen bir metot yardımıyla yarı analitik çözümler bulmaya çalışıyoruz. Optimal perturbasyon iterasyon yöntemini tanıtıyor ve sonra yeniden modifiye edilen ikili Drinfel’d-Sokolov-Wilson denklemine uyguluyoruz. Klasik perturbasyon teorisi ve optimizasyon teknikleri birleştirilerek bu yöntemi inşa ediyoruz. Optimal perturbasyon iterasyon olarak önerilen metodun gücünü göstermek için özel bir örneği derinlemesine irdeliyoruz. Teorem ve uygulamalar önerilen tekniğin ele alınan denklemler için iterasyonun daha ilk basamaklarında tam çözüme hızlı bir şekilde yaklaştığını göstermektedir

References

  • Aktürk, T., Gürefe, Y., Pandır, Y., 2017. An application of the new function method to the Zhiber–Shabat equation, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7(3), 271-274.
  • Bildik, N., Deniz, S., 2017. A new efficient method for solving delay differential equations and a comparison with other methods, The European Physical Journal Plus, 132(1), 51.
  • Bildik, N., Deniz, S., 2018. New analytic approximate solutions to the generalized regularized long wave equations, Bulletin of the Korean Mathematical Society, 55(3), 749-762.
  • Bildik, N., Deniz, S., 2018. Solving the burgers' and regularized long wave equations using the new perturbation iteration technique, Numerical Methods for Partial Differential Equations, 34(5), 1489-1501.
  • Bulut, H., Baskonus, H. M., Pandir, Y., 2013. The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation. In Abstract and Applied Analysis (Vol. 2013). Hindawi.
  • Demiray, S. T., Pandir, Y., Bulut, H., 2016. All exact travelling wave solutions of Hirota equation and Hirota–Maccari system, Optik-International Journal for Light and Electron Optics, 127(4), 1848-1859.
  • Deniz, S., Bildik, N. 2018. Optimal perturbation iteration method for Bratu-type problems, Journal of King Saud University-Science, 30(1), 91-99.
  • Deniz, S. 2017. Optimal perturbation iteration method for solving nonlinear heat transfer equations. Journal of Heat Transfer, 139(7), 074503.
  • Fan, Engui, and Hongqing Zhang., 1998. A note on the homogeneous balance method. Physics Letters A 246(5), 403-406.
  • İnan, İ.E., 2019. Auto-Bäcklund Transformation for Fifth Order Equation of the Burgers Hierarchy, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 19, 021301, 328-334.
  • Inc, M., 2008. The approximate and exact solutions of the space-and time fractional Burgers’ equations with initial conditions by variational iteration method, Journal of Mathematical Analysis and Applications, 345(1), 476-484.
  • Guo, Boling, Liming Ling, and Q. P. Liu., 2012. Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions, Physical Review E, 85(2), 026607.
  • Manafian H.J. and Lakestani M.,2013. Solitary wave and periodic wave solutions for variants of the KdV-Burger and the K(n,n)-Burger equations by the generalized tanh-coth method, Communations in Numerical Analysis, 1–18.
  • Manafian H.J. and Zamanpour I.,2013. Analytical treatment of the coupled Higgs equation and the Maccari system via Exp-function method, Acta Universitatis Apulensis, 33, 203–216.
  • Matveev V.B. and Salle M.A., 1991. Darboux Transformations and Solitons, Springer, Berlin.
  • Malfliet W., 1992. Solitary wave solutions of nonlinear wave equations, American Journal of Physics, 60, 650-654.
  • Shang Y., 2007 Backlund transformation, Lax pairs and explicit exact solutions for the shallow water waves equation. Applied Mathematics and Computation, 187, 1286-1297.
  • Shen S. and Pan Z.,2003. A note on the Jacobi elliptic function expansion method, Physics Letters A, 308, 143-148.
  • Wadati, M., Heiji S., and Kimiaki K., 1975. Relationships among inverse method, Bäcklund transformation and an infinite number of conservation laws. Progress of theoretical physics 53(2) , 419-436.
  • Wazwaz, A.M., 2007. Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method. Applied Mathematics and Computation, 190(1), 633-640.
There are 20 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Sinan Deniz 0000-0002-8884-3680

Publication Date March 17, 2020
Submission Date November 22, 2019
Published in Issue Year 2020 Volume: 20 Issue: 1

Cite

APA Deniz, S. (2020). İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 20(1), 35-40. https://doi.org/10.35414/akufemubid.649745
AMA Deniz S. İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. March 2020;20(1):35-40. doi:10.35414/akufemubid.649745
Chicago Deniz, Sinan. “İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi Ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20, no. 1 (March 2020): 35-40. https://doi.org/10.35414/akufemubid.649745.
EndNote Deniz S (March 1, 2020) İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20 1 35–40.
IEEE S. Deniz, “İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 20, no. 1, pp. 35–40, 2020, doi: 10.35414/akufemubid.649745.
ISNAD Deniz, Sinan. “İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi Ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20/1 (March 2020), 35-40. https://doi.org/10.35414/akufemubid.649745.
JAMA Deniz S. İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2020;20:35–40.
MLA Deniz, Sinan. “İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi Ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 20, no. 1, 2020, pp. 35-40, doi:10.35414/akufemubid.649745.
Vancouver Deniz S. İkili Drinfel’d-Sokolov-Wilson Denklemlerinin Modifiyesi ve Yaklaşık Çözümleri İçin Optimal Perturbasyon İterasyon Metodu. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2020;20(1):35-40.