MEFM For Exact Solutions Of The (3+1) Dimensional KZK Equation and (3+1) Dimensional JM Equation

Year 2021, Volume: 21 Issue: 1, 97 - 105, 24.02.2021

Şeyma Tülüce Demiray , Sevgi Kastal

https://doi.org/10.35414/akufemubid.855854

Cited By: 1

Abstract

In this study, we have applied the modified exp -expansion function method (MEFM) to obtain the exact travelling wave solutions for the (3+1) dimensional Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation and (3+1)-dimensional Jimbo-Miwa (JM) equation. Dark soliton solution, dark-bright soliton solution, hyperbolic function solution and trigonometric function solution of the (3+1) dimensional KZK equation and (3+1)-dimensional JM equation have been found by using this method. After that, we have scratched the 2D and 3D graphs for all exact solutions obtained in this study by using Wolfram Mathematica 9. Thus, the graphical simulations openly show force of this method.

Keywords

The (3+1) dimensional KZK Equation, (3+1)-Dimensional Jimbo-Miwa Equation, MEFM, Dark Soliton Solution, Trigonometric Function Solutions, Hyperbolic Solutions

(3+1) Boyutlu KZK Denklemi ve (3+1) Boyutlu JM Denkleminin Tam Çözümleri için MEFM

Abstract

Bu çalışmada, (3+1) boyutlu Khokhlov – Zabolotskaya – Kuznetsov (KZK) denklemi ve (3+1) boyutlu Jimbo-Miwa (JM) denklemlerinin yürüyen tam dalga çözümlerini elde etmek için, modifiye edilmiş exp -açılım fonksiyon metodunu (MEFM) uyguladık. Bu yöntemle (3+1) boyutlu KZK denkleminin ve (3+1) boyutlu JM denkleminin dark soliton çözümü, dark-bright soliton çözümü, hiperbolik fonksiyon çözümü ve trigonometrik fonksiyon çözümü bulunmuştur. Daha sonra, bu çalışmada elde edilen tüm kesin çözümler için Wolfram Mathematica 9’u kullanarak 2 boyutlu ve 3 boyutlu grafikleri çizdik. Böylece, grafiksel gösterimler bu yöntemin gücünü açıkça göstermektedir.

Keywords

(3 + 1) boyutlu KZK Denklemi, ; (3 + 1) - Boyutlu Jimbo-Miwa Denklemi;, MEFM, Dark Soliton Çözümü, Trigonometrik Fonksiyon Çözümleri, Hiperbolik Çözümler

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