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

Yıl 2021, Cilt: 11 Sayı: 2, 276 - 289, 31.12.2021

Şeyma Tülüce Demiray Sevgi Kastal

https://doi.org/10.37094/adyujsci.857583

Öz

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.

Anahtar Kelimeler

The simplified MCH equation, the Getmanou equation, MEFM, dark optical soliton solutions, dark-bright optical soliton solutions, ; Mathematica

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

Öz

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.

Anahtar Kelimeler

Basitleştirilmiş MCH denklemi, Getmanou denklemi, MEFM, dark optik soliton çözümler, dark-bright optik soliton çözümler, Mathematica

Kaynakça

• [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.