New exact solutions and modulation instability for the nonlinear \((2+1)\)-dimensional Davey-Stewartson system of equation (Q781129)

Summary: The Davey-Stewartson system of equations (DSE) is an equation system that reflects the evolution in finite depth of soft nonlinear packets of water waves that move in one direction but in which the waves' amplitude is modulated in spatial directions. This paper uses the generalized elliptic equation rational expansion technique to extract fresh exact solutions for the DSE. As a consequence, solutions with parameters of trigonometric, hyperbolic and rational function are achieved. To display the physical characteristics of this model, the solutions are graphically displayed. Modulation instability is also discussed, and it is demonstrated that all solutions are accurate and stable.