Rogue Waves in the Generalized Davey-Stewartson System

Abstract

In this study, we consider rogue waves, which appear and disappear suddenly with large amplitudes, in the generalized Davey-Stewartson (GDS) system found in acoustics and discuss their dynamic structure. For the rogue wave solutions, we first obtain the Hirota bilinear form of the GDS system through rational and bilogarithmic transformations. Then, forming the solutions of the GDS system through determinants of matrices, we obtain three types of rogue wave solutions depending on the size of the matrices (\( N\times N \)) and the order of the N-rational solutions: fundamental (line), multi- and higher-order rogue waves. We report the behavior and differences of these three types of rogue waves and explain the change in the waves with respect to time.