Extended Jacobi Elliptic Function Method for the General DSW System: Analytical Solutions, Stability Analysis and Numerical Simulations
Differential Equations and Dynamical Systems, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s12591-026-00795-9
- Dergi Adı: Differential Equations and Dynamical Systems
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Drinfel’d–Sokolov–Wilson (DSW) system, exact solutions, Jacobi elliptic functions, stability analysis, traveling waves
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
In this study, the traveling wave solutions and wave dynamics of the generalized Drinfel’d–Sokolov–Wilson (DSW) system, which is an important model for water wave interactions is investigated. Owing to its integrable structure and physical relevance, the DSW system remains a key model in the study of dispersive hydrodynamics and nonlinear wave propagation. By employing a suitable wave transformation, the system is reduced to a set of ordinary differential equations. To derive exact solutions, the extended Jacobi elliptic function expansion method and the Jacobi elliptic rational function expansion method are applied. The qualitative behavior of these solutions is explored through comprehensive two- and three-dimensional numerical simulations carried out in Maple™ under various parameter settings. Given their rich mathematical structure and broad applicability, Jacobi elliptic functions are particularly effective in modeling phenomena such as water waves, tides, and acoustic waves. Finally, a stability analysis is conducted to verify the physical reliability and robustness of the obtained solutions.