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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2026 / Cilt: 21 Sayı: 1

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

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

Şeyma Tülüce Demiray(OSMANIYE KORKUT ATA UNIVERSITY, DEPARTMENT OF MATHEMATICS)0000-0002-8027-7290
Sevgi Kastal(OSMANIYE KORKUT ATA UNIVERSITY)0000-0001-9152-3023
Pages
97–105
Publication Date
2021-02-24
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AI Summary & Key Takeaways

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

Thus, the graphical simulations openly show force of this method.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact:Thus, the graphical simulations openly show force of this method.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:(3 + 1) boyutlu KZK Denklemi · (3 + 1) - Boyutlu Jimbo-Miwa Denklemi · MEFM

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.

Özet

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.

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Cite This Article

Demiray, Ş. T., Kastal, S. (2021). MEFM For Exact Solutions Of The (3+1) Dimensional KZK Equation and (3+1) Dimensional JM Equation. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 21 Sayı: 1, 97–105. https://doi.org/10.35414/akufemubid.855854

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