Akademik Veri Yönetim Sistemi
Qualitative Theory of Dynamical Systems, cilt.24, sa.4, 2025 (SCI-Expanded, Scopus)
This study investigates the (n+1)-dimensional generalized Kadomtsev–Petviashvili equation, which models important phenomena in fluid dynamics, plasma physics, Bose–Einstein condensates, optical systems, and other physical contexts. Understanding the analytical solutions of the (n+1)-dimensional generalized Kadomtsev–Petviashvili equation is crucial for revealing the wave behavior in these systems and for advancing practical applications. To achieve this, we employ two powerful analytical methods: the modified extended tanh expansion method and the G′G2-expansion function method. These techniques are applied to derive various exact solutions, including hyperbolic, trigonometric, and rational forms. The significant results include a wide range of new analytical solutions, accompanied by graphical representations illustrating their wave dynamics under varying parameters. These findings enhance the understanding of the (n+1)-dimensional generalized Kadomtsev–Petviashvili equation’s behavior across different physical conditions. For the first time, this study presents a unified approach that integrates the modified extended tanh expansion method with the G′G2-expansion function method, thus advancing beyond previous efforts in the literature. This novel combination of two analytical methods enables the discovery of a richer set of solutions and provides deeper insights into complex nonlinear wave phenomena, offering valuable tools for future research in fluid dynamics, plasma physics, and soliton theory. The results open new avenues for future research and contribute to the study of various bodily systems. To the best of our knowledge, this is the first time these methods have been applied for this equation. The scientific validity of each solutions are verified using the Maple software tool.