Nonlinear dynamics of wave structures for the Davey–Stewartson system: a truncated Painlevé approach

The Davey–Stewartson system is a mathematical model that captures the behavior of two-dimensional waves, encompassing key factors like dispersion, nonlinearity, and wave-wave interactions. This work investigates the (2+1) dimensional integrable Davey–Stewartson system by employing the truncated Painlevé analysis. The results are derived using random functions, which are then applied to provide different localized solutions, including rogue waves, dromion-pair, and dromions. Selecting appropriate beginning values for the arbitrary functions also results in the generation, analysis, and visual display of the collisional behavior of these solutions. We find that while rogue waves happen to be unstable in nature, dromions undergo inelastic collisions that exchange both their energy and phase. These findings enhance our understanding of complex wave dynamics and have intriguing applications in fluid dynamics, oceanography, nonlinear optics, and the investigation of nonlinear phenomena in diverse physical systems. It is significant to mention that Maple software is utilized to generate and validate the reliability and precision of all calculations and depictions. All things considered, this work contributes to our understanding of complex nonlinear systems and the role starting conditions play in determining their behavior.