Abstract
In this study, the \((4+1)\) -dimensional Davey-Stewartson-Kadomtsev-Petviashvili equation is analyzed to model internal wave interactions with both elastic and inelastic properties. The investigation begins with the derivation of explicit N-soliton solutions, particularly in the form of bright solitons, which demonstrate localized energy concentration. Subsequently, various breather solutions are proposed in distinct planes using the complex conjugate approach. By employing the long-wave limit approach to the N-soliton solutions, higher-order bright lump and line rogue wave solutions, which represent localized structures and sudden energy surges, are constructed. A novel aspect of this research is the derivation of six distinct hybrid solutions, combining solitons, lumps, and breathers waves through the selection of specific parameters. Physical collision phenomena among these waves, including soliton-soliton and soliton-lump interactions, are explored in detail. A comparative analysis of solution behaviors is conducted for the first time, with overlapping regions and distinctions within their solution spaces highlighted using data points. To analyze the characteristics of these interaction solutions, the results are visually illustrated through 3D and 2D plots. Through this study, significant contributions are made to soliton theory and nonlinear wave research, enhancing the theoretical framework and introducing innovative methods for analyzing wave dynamics.
Graphical abstract
