Some New Soliton Solutions of Time Fractional Resonant Davey–Stewartson Equations

In this study, the Bernoulli subequation method (BS-EM) is applied to investigate the traveling wave solutions of the (2 + 1)-dimensional resonant Davey–Stewartson system. By employing a wave transformation, the system’s nonlinear partial differential equation is reduced to a nonlinear ordinary differential equation, which is then solved using the BS-EM approach. As a result, several new traveling wave solutions, which have not been previously reported in the literature, have been successfully obtained. These solutions provide new insights into the physical dynamics of the system and also satisfy the (2 + 1)-dimensional time–fractional resonant Davey–Stewartson equation. Furthermore, the analytical and graphical analyses of the obtained solutions have been carried out, and the wave profiles have been examined under various parameter conditions. All computations and graphical visualizations in this study were performed using the Wolfram Mathematica 12 software.