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Analytical Solutions for the Generalized (2+1)-D Shallow Water Wave Equation via a Novel Generalized Abel Equation with Variable Coefficients | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 دی 1404 اصل مقاله (4.24 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.67447.3217 | ||
| نویسندگان | ||
| Mir Sajjad Hashemi1؛ Mustafa Bayram2؛ Farzaneh Alizadeh* 3؛ Samad Kheybari* 4؛ Kamyar Hosseini5 | ||
| 11. Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.\\ 2. Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan. | ||
| 2Computer Engineering, Biruni University, Istanbul, Turkey. | ||
| 3Department of Mathematics, Near East University TRNC, Mersin10, Nicosia 99138, Turkey. | ||
| 4Faculty of Art and Science, University of Kyrenia, TRNC, Mersin 10, Turkey. | ||
| 51. Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan.\\ 2. Department of Mathematics, Near East University TRNC, Mersin10, Nicosia 99138, Turkey. | ||
| چکیده | ||
| This study utilizes the generalization of the second-degree Abel equation (SDAE) method with variable coefficients, initially introduced in \cite{hashemi2024variable}, to analyze the generalized (2+1)-D shallow water wave (SWW) equation. Unlike conventional approaches that predominantly rely on constant-coefficient ordinary differential equations (ODEs) or auxiliary ODEs, the proposed method incorporates ODEs with variable coefficients within a sub-equation framework, thereby enhancing its adaptability to nonlinear wave equations. The governing nonlinear partial differential equation (PDE) is first reduced to an ODE, which is then analyzed using this method. Subsequently, various singular and periodic wave solutions are derived, and their dynamic behavior is thoroughly examined. The efficacy of this approach is demonstrated through its successful application to the SWW equation, resulting in exact analytical solutions. This method provides a systematic and efficient framework for solving complex nonlinear PDEs, establishing it as a valuable tool in the study of wave propagation in fluid dynamics. Furthermore, its versatility suggests broad applicability to a range of mathematical physics models, thereby expanding the scope of analytical solution techniques. | ||
| کلیدواژهها | ||
| Generalized (2+1)-D shallow water wave equation؛ Exact solution؛ Generalized Abel equation | ||
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آمار تعداد مشاهده مقاله: 24 تعداد دریافت فایل اصل مقاله: 26 |
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