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Journals / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 16 Sayı: 3

New Analytical Soliton Molecule Solutions of the Conformable Time-Fractional Sharma-Tasso-Olver-Burgers Equation Using Modified Kudryashov Method

Uyumlu Zaman-Kesirli Sharma-Tasso-Olver-Burgers Denkleminin Modifiye Kudryashov Yöntemi ile Yeni Analitik Soliton Molekül Çözümleri

Fatih Maraşlı(SELÇUK ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ)0009-0008-4563-752X
Muammer Ayata(Selçuk University)0000-0001-9436-6414
Pages
1242–1255
Publication Date
2026-09-01
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AI Summary & Key Takeaways

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

Furthermore, the obtained results make significant contributions to the understanding of soliton molecules in fractional-order systems, opening new research avenues in fields such as quantum field theory, plasma physics, and nonlinear optics.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, novel analytical soliton molecule solutions for the conformable time-fractional Sharma-Tasso-Olver-Burgers (STOB) equation have been obtained using the modified Kudryashov method for the first time.
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Key Findings & Data:The conformable fractional derivative approach used in our study allows accurate modeling of anomalous dynamic behaviors and fractional scaling in physical systems, while showing how changes in the fractional derivative order affect dynamic evolution.
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Conclusion & Impact:Furthermore, the obtained results make significant contributions to the understanding of soliton molecules in fractional-order systems, opening new research avenues in fields such as quantum field theory, plasma physics, and nonlinear optics.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Modifiye Kudryashov yöntemi · Uyumlu kesirli türev · Sharma-Tasso-Olver-Burgers denklemi

Abstract

In this study, novel analytical soliton molecule solutions for the conformable time-fractional Sharma-Tasso-Olver-Burgers (STOB) equation have been obtained using the modified Kudryashov method for the first time. The STOB equation is an important nonlinear differential equation that combines the well-known Burgers and Sharma-Tasso-Olver (STO) equations, showing rich soliton molecular behavior. Our solutions reveal previously unknown soliton molecule structures with unique nonlinear dynamics that go beyond classical Burgers and STO equations. Through systematic application of the modified Kudryashov method, we obtain multiple families of exact solutions with different characteristics, including single-kink wave profiles and solitary wave solutions with different characteristics. The conformable fractional derivative approach used in our study allows accurate modeling of anomalous dynamic behaviors and fractional scaling in physical systems, while showing how changes in the fractional derivative order affect dynamic evolution. We discover different dynamical behaviors ranging from subdiffusive to classical dynamics across a broad spectrum, depending on the fractional derivative order value. The obtained solutions have potential applications in various physical systems, from mode-locked fiber lasers to anomalous diffusion processes, and from slow light propagation in optical fibers to Bose-Einstein condensates. The evolution of these solutions is examined through comprehensive graphical analysis. 3D surfaces, contour maps, and 2D cross-sectional plots are utilized to illustrate the physical impact of the fractional order α. These visualizations confirm that the wave profiles maintain their stability while exhibiting distinct fractional dynamics as they propagate. Furthermore, the obtained results make significant contributions to the understanding of soliton molecules in fractional-order systems, opening new research avenues in fields such as quantum field theory, plasma physics, and nonlinear optics.

Özet

Bu çalışmada, uyumlu zaman-kesirli Sharma-Tasso-Olver-Burgers (STOB) denklemi için yeni analitik soliton molekül çözümleri, modifiye Kudryashov yöntemi kullanılarak ilk kez elde edilmiştir. STOB denklemi, iyi bilinen Burgers ve Sharma-Tasso-Olver (STO) denklemlerini birleştiren ve zengin soliton moleküler davranış gösteren önemli bir nonlineer diferansiyel denklemdir. Çözümlerimiz, klasik Burgers ve STO denklemlerinin ötesine geçen benzersiz nonlineer dinamiklere sahip, daha önce bilinmeyen soliton molekül yapılarını ortaya koymaktadır. Modifiye Kudryashov yönteminin sistematik uygulaması yoluyla; tek-kink dalga profilleri ve farklı özelliklere sahip soliter dalga çözümleri dahil olmak üzere, farklı özelliklere sahip çoklu tam çözüm aileleri elde edilmektedir. Çalışmamızda kullanılan uyumlu kesirli türev yaklaşımı, fiziksel sistemlerdeki anomal dinamik davranışların ve kesirli ölçeklemenin doğru modellenmesine olanak sağlarken, kesirli türev mertebesindeki değişikliklerin dinamik evrimi nasıl etkilediğini göstermektedir. Kesirli türev mertebe değerine bağlı olarak, subdifüzif dinamikten klasik dinamiklere kadar geniş bir spektrumda farklı dinamik davranışlar keşfetmekteyiz. Elde edilen çözümler; mod-kilitli fiber lazerlerden anomal difüzyon süreçlerine ve optik fiberlerde yavaş ışık yayılımından Bose-Einstein yoğuşuklarına kadar çeşitli fiziksel sistemlerde potansiyel uygulamalara sahiptir. Bu çözümlerin evrimi, kapsamlı grafiksel analiz yoluyla incelenmiştir. Kesirli mertebe α'nın fiziksel etkisini örneklendirmek için 3B yüzeyler, kontur haritaları ve 2B kesit grafikleri kullanılmıştır. Bu görselleştirmeler, dalga profillerinin yayılırken belirgin kesirli dinamikler sergilemesine rağmen kararlılıklarını koruduklarını doğrulamaktadır. Ayrıca, elde edilen sonuçlar kesirli-mertebe sistemlerdeki soliton moleküllerinin anlaşılmasına önemli katkılar sağlamakta; kuantum alan teorisi, plazma fiziği ve nonlineer optik gibi alanlarda yeni araştırma yolları açmaktadır.

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Cite This Article

Maraşlı, F., Ayata, M. (2026). New Analytical Soliton Molecule Solutions of the Conformable Time-Fractional Sharma-Tasso-Olver-Burgers Equation Using Modified Kudryashov Method. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 16 Sayı: 3, 1242–1255. https://doi.org/10.21597/jist.1814221

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