Analysis of Chaos and Solitons Stability in the (2+1)-Dimensional Sakovich Equation for Nonlinear Wave Motion
Applied Mathematics and Information Sciences, cilt.20, sa.5, ss.1245-1259, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 20 Sayı: 5
- Basım Tarihi: 2026
- Doi Numarası: 10.18576/amis/200510
- Dergi Adı: Applied Mathematics and Information Sciences
- Derginin Tarandığı İndeksler: Scopus, zbMATH
- Sayfa Sayıları: ss.1245-1259
- Anahtar Kelimeler: 2-dSE, Analytical methods, Chaos and Stability, Energy Conservation, Fluid Dynamics, Periodic solutions, Solitons
- Karadeniz Teknik Üniversitesi Adresli: Hayır
Özet
In this work, the nonlinear dynamics and soliton structures of the integrable (2+1)-dimensional Sakovich equation (2-dSE), which arises in nonlinear wave propagation and fluid dynamics, are investigated. This equation effectively models describes nonlinear wave phenomena in shallow water and stratified fluids, including wave breaking, soliton formation, and periodic wave patterns. By employing the extended simplest equation and the Φ^6-model expansion methods, several new families of exact analytical solutions are derived, including solitary waves, periodic structures, kink and anti-kink solitons, breather-type waves, and multi-peak solitons. These methods effectively handle the nonlinearities in the model and provide a systematic framework for deriving closed-form solutions. The dynamical behavior of the model is further explored through chaotic analysis under external perturbations, revealing the system?s sensitivity, long-term evolution, and complex dynamics. In addition, conservation laws are derived to identify key invariants governing the equation, and modulational instability analysis confirms the stability and physical relevance of the obtained solutions. Graphical simulations are presented to illustrate the dynamical features, stability regimes, and diverse soliton structures. In particular, Figures support the main objectives of this work by clearly demonstrating the analytically constructed soliton families, their dynamical behavior, and their physical relevance in nonlinear wave propagation. The analytical and numerical results demonstrate the effectiveness of the proposed methods in generating rich classes of exact solutions for complex multidimensional nonlinear partial differential equations.