Dynamics of novel soliton and periodic solutions to the coupled fractional nonlinear model

Abstract

This study secures the soliton solutions of the (2+1)-dimensional Davey–Stewartson equation (DSE) incorporating the properties of the truncated M-fractional derivative. The DSE and its coupling with other systems have extensive applications in many fields, including physics, applied mathematics, engineering, hydrodynamics, plasma physics, and nonlinear optics. Various solutions, such as dark, singular, bright-dark, bright, complex, and combined solitons, are derived. In addition, exponential, periodic, and hyperbolic solutions are also generated. The newly designed integration method, known as the modified Sardar subequation method (MSSEM), has been applied in this study for extracting the solutions. The approach is efficient in explaining fractional nonlinear partial differential equations (FNLPDEs) by confirming pre-existing solutions and producing new ones. Furthermore, we plot the density, 2D, and 3D graphs with the associated parameter values to visualize the solutions. The outcomes of this work indicate the effectiveness of the method utilized to improve nonlinear dynamical behavior. We anticipate that our work will be helpful for a large number of engineering models and other related problems. © 2024 The Author(s)