Fractional dynamics of wave packets: solving the Davey-Stewartson equation with computational method

In this study, the fractional Davey-Stewartson equation, a fundamental nonlinear model describing wave packet dynamics in various physical contexts, is investigated. The Riccati-Bernoulli sub-ODE algorithm, combined with the Bäcklund transformation, is employed to obtain new exact solutions expressed in trigonometric, hyperbolic, and rational function forms. The solutions give an entire spectrum of the wave figures such as quasi-periodic and cnoidal wave forms that can provide more information on the wave dynamics in the systems of the fractional-order. The influence of the fractional parameter α on the behavior of the waves is studied where the variety of changes in the structures of solutions is significantly represented. Graphical depictions are also made in the study and include 2D, 3D, and contour plots, which evidently explain the influence of fractional dynamics and the interaction between the waves. This paper, by integrating an analytical solution with a numerical one, will give a better interpretation on the processes of waves in fractional nonlinear media. The results have a contribution to the overall theory on fractional-order differential equations and its applicability in mathematical physics and engineering.