Propagation of Optical Solitons to the Fractional Resonant Davey-Stewartson Equations

In this work, we investigate the exact solutions of (2+1)-dimensional coupled resonant Davey-Stewartson equation (DSE) with the properties of truncated M-fractional derivative. It is a significant equation system that models wave packets in different fields. DSE and its coupling with other system have interesting properties and many applications in the fields of nonlinear sciences. The concept of resonant is quite important in optics, plasma physics, magneto-acoustic waves and fluid dynamics. In order to use newly designed integration method known as modified Sardar subequation method (MSSEM), we first convert the (2+1)-dimensional fractional coupled resonant DSE into a set of nonlinear ordinary diferential equations. To acquire the exact solutions, the ordinary differential equation is solved by applying the homogeneous balance method between the highest power terms and the highest derivative of the ordinary differential equation. The optical soliton solutions of the resultant system are investigated using different cases and physical constant values. The aforementioned technique is applied to the considered model, yielding several kinds of soliton solutions, such as mixed, dark, singular, bright-dark, bright, complex and combined solitons. In addition, exponential, periodic, and hyperbolic solutions are also obtained. Also, we plot the 2D, and 3D graphs with the associated parameter values to visualize the solutions. The findings of this work will help to identify and clarify some novel soliton solutions and it is expected that the solutions obtained will play a vital role in the fields of physics and engineering.