Document Type : Research Paper
Authors
1
1. Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.\\ 2. Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan.
2
Computer Engineering, Biruni University, Istanbul, Turkey.
3
Department of Mathematics, Near East University TRNC, Mersin10, Nicosia 99138, Turkey.
4
Faculty of Art and Science, University of Kyrenia, TRNC, Mersin 10, Turkey.
5
1. Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan.\\ 2. Department of Mathematics, Near East University TRNC, Mersin10, Nicosia 99138, Turkey.
10.22034/cmde.2025.67447.3217
Abstract
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.
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