Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

ÖNDER İ., SEÇER A., BAYRAM M.

Physica Scripta, cilt.99, sa.1, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 99 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1088/1402-4896/ad10f6
  • Dergi Adı: Physica Scripta
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Chemical Abstracts Core, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: modified Korteweg-de Vries Zakharov-Kuznetsov equation, new Kudryashov method, soliton solution, unified Riccati equation expansion method
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we explore analytical solutions for the (3+1)-dimensional time-fractional modified Korteweg-de Vries Zakharov-Kuznetsov equation, which incorporates a conformable derivative. Our interest in this model is driven by its significant role in simulating ion-acoustic waves in magnetized plasma. We adopt the unified Riccati equation expansion method and the new Kudrashov method to discover soliton solutions. Our approach uncovers various soliton types, such as kink, singular, periodic-singular, and bright solitons. We conduct a thorough analysis of how different parameters affect wave propagation, enhancing our study with descriptive figures and insightful observations. Furthermore, we delve into the modulation instability characteristic of this model. The influence of specific parameters, like wave number and the order of the conformable derivative, on wave dynamics is demonstrated through detailed visualizations. We also present 2D and 3D graphical representations of these solutions.