On the new sine-Gordon solitons of the generalized Korteweg-de Vries and modified Korteweg-de Vries models via beta operator
Yazarlar (4)
Binzhou Polytechnic, Çin
University of Toledo, Amerika Birleşik Devletleri
Doç. Dr. Esin İLHAN
Kırşehir Ahi Evran Üniversitesi, Türkiye
Harran University, Türkiye
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Aims Mathematics (Q1) | ||
| Dergi ISSN | 2473-6988 Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | İngilizce | Basım Tarihi | 03-2025 |
| Cilt / Sayı / Sayfa | 10 / 3 / 5456–5479 | DOI | 10.3934/math.2025252 |
| Makale Linki | https://www.aimspress.com/article/doi/10.3934/math.2025252 | ||
| Özet |
| In this paper, we applied the sine-Gordon expansion method (SGEM) and the rational sine-Gordon expansion method (RSGEM) for obtaining some new analytical solutions of the (2+1)-dimensional generalized Korteweg-de Vries (gKdV) and modified Korteweg-de Vries (mKdV) equations with a beta operator. The sine-Gordon expansion method (SGEM) has recently been extended to a rational form, referred to as the rational sine-Gordon expansion method (RSGEM). By applying a specific transformation, the equations are reduced to a nonlinear ordinary differential equation (NODE), allowing for the derivation of analytical solutions in various forms, including complex, hyperbolic, rational, and exponential. All these solutions are expressed through periodic functions using SGEM and RSGEM. The physical significance of the parametric dependencies of these solutions is also examined. Additionally, several simulations, including three-diemensional (3D) visualizations and revolutionary wave behaviors, are presented, based on different parameter selections. Revolutionary surfaces, defined by height and radius as independent variables, are extracted to further illustrate the wave dynamics. |
| Anahtar Kelimeler |
| gKdV equation | mKdV equation | beta operator | analytical method | analytic solutions Mathematics Subject Classification |