Akademik Veri Yönetim Sistemi
INDIAN JOURNAL OF PHYSICS, 2025 (SCI-Expanded, Scopus)
This research specializes in obtaining new solitary wave solutions to a generalized shallow water type equation. This equation is a very important model in fluid dynamics that characterizes different dynamics of shallow water waves under varying conditions. In this work, the Auto-B & auml;cklund transformation associated with the equation was established by using the extended homogeneous balance technique in conjunction with the symbolic computing powers of Maple. The latter approach facilitated the systematic derivation of several explicit solutions, which serve as a basis for better understanding the dynamics of the equation. Furthermore, by utilizing the extended transformed rational function approach, we explore a broader class of solutions and successfully identify complexiton solutions-special types of wave structures that exhibit both solitary and oscillatory characteristics. To provide deeper insight into the obtained results, we present three-dimensional graphical representations that highlight the physical significance and dynamic behavior of the solutions. These visualizations offer a clearer understanding of the wave phenomena described by the generalized shallow-water-like equation and highlight the effectiveness of our analytical techniques in solving nonlinear partial differential equations.