Fractional Solitons for Controlling Wave Dynamics in Fluids and Plasmas

This paper presents soliton solutions of the fractional (2+1)-dimensional Davey–Stewartson equation based on a local fractional derivative to represent wave packet propagation in dispersive media under both spatial and temporal effects. The importance of this work is in demonstrating how fractional derivatives represent a more capable modeling tool compared to conventional integer-order methods since they include anomalous dispersion, nonlocal interactions, and memory effects typical in most physical systems in nature. The main objective of this research is to build and examine a broad family of soliton solutions such as bright, dark, singular, bright–dark, and periodic forms, and to explore the influence of fractional orders on their amplitude, width, and dynamical stability. Specific focus is given to the comparison of the behavior of fractional-order solutions with that of traditional integer-order models so as to further the knowledge on fractional calculus and its role in governing nonlinear wave dynamics in fluids, plasmas, and other multifunctional media. Methodologically, this study uses the fractional complex transform together with a new mapping technique, which transforms the fractional Davey–Stewartson equation into solvable nonlinear ordinary differential equations. Such a systematic methodology allows one to derive various families of solitons and form a basis for investigation of nonlinear fractional systems in the general case. Numerical simulations, given in the form of three-dimensional contour maps, density plots, and two-dimensional, demonstrate stability and propagation behavior of the derived solitons. The findings not only affirm the validity of the devised analytic method but also promise possibilities of useful applications in fluid dynamics, plasma physics, and nonlinear optics, where wave structure manipulation using fractional parameters can result in increased performance and novel capabilities.