Davey-Stewartson system and investigation of the impacts of the nonlinearity

Abstract

This study examines for the first time the adapted parabolic law nonlinearity form of (2+1)-dimensional Davey-Stewartson system, an important equation modeling the surface water wave packets with finite depth. For the first time, we will investigate the parabolic law nonlinearity form. Not only is this a significant aspect, but we will also explore it with various parameter values to see its impact on soliton dynamics. In order to transform the nonlinear partial differential equation into a form for which the analytical method can be applied, the ordinary differential equation structure obtained by first applying wave transformation. In the following stage, we implement the new Kudryashov method and sinh-Gordon equation expansion techniques to retrieve bright, dark, singular, and different types of kink solitons. The effect of parabolic law nonlinearity parameters on the obtained soliton types has also been examined. We illustrate the 3D and 2D graphs of some of the obtained solutions to gain a physical perspective. The study will contribute to the literature in terms of the form of the examined problem, its content and results, and the effectiveness of the applied methods.