EXPLORATION OF FRACTIONAL EFFECTS AND MULTI-STABILITY IN THE NONLINEAR (2+1)-DIMENSIONAL DAVEY-STEWARTSON FOKAS SYSTEM

This work delves into a profound analysis of the fractional Davey-Stewartson Fokas system, which has applications in analyzing two-dimensional wave packets on water surfaces and modeling pulse propagation in optical fibers. An in-depth comparative study is conducted on the local M and the fractional beta derivatives to elucidate their effects on the system's solutions and to investigate the role of fractional parameters in shaping the system's behavior. Two approaches, the $ G'/(bG'+G+a) $ expansion and the Sardar sub-equation approaches, are employed to generate new solitary wave solutions that appear in the form of lump, periodic, singular, bright, and their combo solitons. The solutions are produced under constraint conditions and illustrated using 3D, density, and 2D plots by selecting appropriate values of parameters. Moreover, chaotic phenomena are analyzed through the observation of multi-stability by setting the parameters and varying initial conditions. The extracted solutions validate the effectiveness of the proposed methodologies in deriving exact solutions in nonlinear contexts.