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Basitleştirilmiş MCH Denklemi ve Getmanou Denkleminin Tam Çözümleri için Modifiye Edilmiş Exp (-vartheta(sigma))-Açılım Fonksiyon Metodu

Year 2021, Volume 11, Issue 2, 276 - 289, 31.12.2021
https://doi.org/10.37094/adyujsci.857583

Abstract

Mevcut araştırma, Modifiye edilmiş exp -açılım fonksiyon metodunu (MEFM), basitleştirilmiş MCH denklemi ve Getmanou denklemi için tam hareketli dalga çözümlerini elde etmek üzere uygulayarak test eder. Basitleştirilmiş MCH denkleminin ve Getmanou denkleminin dark optik soliton ve dark-bright optik soliton çözümleri bu yöntem kullanılarak başarıyla elde edilmiştir. Bu çalışmadaki tüm hesaplamalar Wolfram Mathematica 9 tarafından yapılmış ve 2D ve 3D grafikleri çizilmiştir. Ayrıca, grafiksel gösterim bu yöntemin açıkça gücünü göstermektedir.

References

  • [1] Ali, A., Aly, R.S., Dianchen, L., Dispersive solitary wave soliton solutions of (2 + 1)-dimensional Boussineq dynamical equation via extended simple equation method, Journal of King Saud University – Science, 31, 653–658, 2019.
  • [2] Lu, D., Seadawy, A.R, Ali, A., Applications of extended simple equationmethod on unstable nonlinear Schrödinger equations, Optik, 140, 136-144, 2017.
  • [3] Bekir, A., Zahran, E., Three distinct and impressive visions for the soliton solutions to the higher-order nonlinear Schrodinger equation, Optik, 228(3), 166157, 2021.
  • [4] Nisar, S.K., Ilhan, O.A., Abdulazeez, S.T., Manafian, J.M., Osman, M.S., Novel multiple soliton solutions for some nonlinear PDEs via multiple Exp-function method, Results in Physics, 21, 103769, 2021.
  • [5] Tuluce Demiray, S., Pandır, Y., Bulut, H., All exact travelling wave solutions of Hirota equation and Hirota-Maccari system, Optik, 127, 1848-1859, 2016.
  • [6] Tuluce Demiray, S., New soliton solutions of optical pulse envelope E(Z, τ) with Beta Time Derivative, Optik , 223, 165453, 2020.
  • [7] Koçak, Z.F., Bulut, H., Koc, D.A., Başkonuş, H.M., Prototype traveling wave solutions of new coupled Konno-Oono equation, Optik, 127, 10786-10794, 2016.
  • [8] Tuluce Demiray, S., Kastal, S., Dark-Bright optical soliton solutions of (3+1)-dimensional modified quantum Zakharov-Kuznetsov equation, Turkish Journal of Mathematics and Computer Science, 11, 90-94, 2019.
  • [9] Hossain, A.K.M.K.S., Akbar, M.A., Solitary wave solutions of few nonlinear evolution equations, AIMS Mathematics, 5, 1119-1215, 2020.
  • [10] Irshad, A., Usman, M., Mohyud-Din, S.T., Exp-function method for simplified modified Camassa-Holm equation, International Journal of Medern Mathematical Sciences, 4(3), 146-155, 2012.
  • [11] Wazwaz, A., New compact and noncompact solutions for two variants of a modified Camassa–Holm equation, Applied Matematics and Computations, 163 (3) ,1165–1179, 2005.
  • [12] Yang, L., Application of trial equation method for solving the Getmanou equation, Applied Mathematics, 5, 1463-1473, 2014.
  • [13] Fan, X.F., Classification of all single traveling-wave solutions to Getmanou equation , FIZIKI A, 19, 191-196, 2011.
  • [14] Tuluce Demiray, S., Pandır, Y., Bulut, H., New solitary wave solutions of Maccari system, Ocean Engineering, 103, 153-159, 2015.

The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation

Year 2021, Volume 11, Issue 2, 276 - 289, 31.12.2021
https://doi.org/10.37094/adyujsci.857583

Abstract

The present research explores, the modified exp -expansion function method (MEFM) is tested by applying it to obtain the exact travelling wave solutions for the simplified MCH equation and the Getmanou equation. Dark optical soliton solutions and dark-bright optical soliton solutions of the simplified MCH equation and the Getmanou equation are successfully constructed by using this method. We carry out all the computations and draw the 2D and 3D graph in this paper by Wolfram Mathematica 9. Besides, the graphical representation obviously shows forcefulness of this method.

References

  • [1] Ali, A., Aly, R.S., Dianchen, L., Dispersive solitary wave soliton solutions of (2 + 1)-dimensional Boussineq dynamical equation via extended simple equation method, Journal of King Saud University – Science, 31, 653–658, 2019.
  • [2] Lu, D., Seadawy, A.R, Ali, A., Applications of extended simple equationmethod on unstable nonlinear Schrödinger equations, Optik, 140, 136-144, 2017.
  • [3] Bekir, A., Zahran, E., Three distinct and impressive visions for the soliton solutions to the higher-order nonlinear Schrodinger equation, Optik, 228(3), 166157, 2021.
  • [4] Nisar, S.K., Ilhan, O.A., Abdulazeez, S.T., Manafian, J.M., Osman, M.S., Novel multiple soliton solutions for some nonlinear PDEs via multiple Exp-function method, Results in Physics, 21, 103769, 2021.
  • [5] Tuluce Demiray, S., Pandır, Y., Bulut, H., All exact travelling wave solutions of Hirota equation and Hirota-Maccari system, Optik, 127, 1848-1859, 2016.
  • [6] Tuluce Demiray, S., New soliton solutions of optical pulse envelope E(Z, τ) with Beta Time Derivative, Optik , 223, 165453, 2020.
  • [7] Koçak, Z.F., Bulut, H., Koc, D.A., Başkonuş, H.M., Prototype traveling wave solutions of new coupled Konno-Oono equation, Optik, 127, 10786-10794, 2016.
  • [8] Tuluce Demiray, S., Kastal, S., Dark-Bright optical soliton solutions of (3+1)-dimensional modified quantum Zakharov-Kuznetsov equation, Turkish Journal of Mathematics and Computer Science, 11, 90-94, 2019.
  • [9] Hossain, A.K.M.K.S., Akbar, M.A., Solitary wave solutions of few nonlinear evolution equations, AIMS Mathematics, 5, 1119-1215, 2020.
  • [10] Irshad, A., Usman, M., Mohyud-Din, S.T., Exp-function method for simplified modified Camassa-Holm equation, International Journal of Medern Mathematical Sciences, 4(3), 146-155, 2012.
  • [11] Wazwaz, A., New compact and noncompact solutions for two variants of a modified Camassa–Holm equation, Applied Matematics and Computations, 163 (3) ,1165–1179, 2005.
  • [12] Yang, L., Application of trial equation method for solving the Getmanou equation, Applied Mathematics, 5, 1463-1473, 2014.
  • [13] Fan, X.F., Classification of all single traveling-wave solutions to Getmanou equation , FIZIKI A, 19, 191-196, 2011.
  • [14] Tuluce Demiray, S., Pandır, Y., Bulut, H., New solitary wave solutions of Maccari system, Ocean Engineering, 103, 153-159, 2015.

Details

Primary Language English
Subjects Mathematics, Applied
Journal Section Mathematics
Authors

Şeyma TÜLÜCE DEMİRAY (Primary Author)
OSMANIYE KORKUT ATA UNIVERSITY, DEPARTMENT OF MATHEMATICS
0000-0002-8027-7290
Türkiye


Sevgi KASTAL
OSMANIYE KORKUT ATA UNIVERSITY
0000-0001-9152-3023
Türkiye

Publication Date December 31, 2021
Application Date January 10, 2021
Acceptance Date September 10, 2021
Published in Issue Year 2021, Volume 11, Issue 2

Cite

Bibtex @research article { adyujsci857583, journal = {Adıyaman University Journal of Science}, issn = {2147-1630}, eissn = {2146-586X}, address = {}, publisher = {Adıyaman University}, year = {2021}, volume = {11}, number = {2}, pages = {276 - 289}, doi = {10.37094/adyujsci.857583}, title = {The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation}, key = {cite}, author = {Tülüce Demiray, Şeyma and Kastal, Sevgi} }
APA Tülüce Demiray, Ş. & Kastal, S. (2021). The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation . Adıyaman University Journal of Science , 11 (2) , 276-289 . DOI: 10.37094/adyujsci.857583
MLA Tülüce Demiray, Ş. , Kastal, S. "The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation" . Adıyaman University Journal of Science 11 (2021 ): 276-289 <https://dergipark.org.tr/en/pub/adyujsci/issue/67254/857583>
Chicago Tülüce Demiray, Ş. , Kastal, S. "The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation". Adıyaman University Journal of Science 11 (2021 ): 276-289
RIS TY - JOUR T1 - The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation AU - Şeyma Tülüce Demiray , Sevgi Kastal Y1 - 2021 PY - 2021 N1 - doi: 10.37094/adyujsci.857583 DO - 10.37094/adyujsci.857583 T2 - Adıyaman University Journal of Science JF - Journal JO - JOR SP - 276 EP - 289 VL - 11 IS - 2 SN - 2147-1630-2146-586X M3 - doi: 10.37094/adyujsci.857583 UR - https://doi.org/10.37094/adyujsci.857583 Y2 - 2021 ER -
EndNote %0 Adıyaman University Journal of Science The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation %A Şeyma Tülüce Demiray , Sevgi Kastal %T The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation %D 2021 %J Adıyaman University Journal of Science %P 2147-1630-2146-586X %V 11 %N 2 %R doi: 10.37094/adyujsci.857583 %U 10.37094/adyujsci.857583
ISNAD Tülüce Demiray, Şeyma , Kastal, Sevgi . "The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation". Adıyaman University Journal of Science 11 / 2 (December 2021): 276-289 . https://doi.org/10.37094/adyujsci.857583
AMA Tülüce Demiray Ş. , Kastal S. The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation. ADYU J SCI. 2021; 11(2): 276-289.
Vancouver Tülüce Demiray Ş. , Kastal S. The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation. Adıyaman University Journal of Science. 2021; 11(2): 276-289.
IEEE Ş. Tülüce Demiray and S. Kastal , "The Modified Exp (-ϑ(σ))-Expansion Function Method for Exact Solutions of the Simplified MCH Equation and the Getmanou Equation", Adıyaman University Journal of Science, vol. 11, no. 2, pp. 276-289, Dec. 2021, doi:10.37094/adyujsci.857583

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