Bäcklund Transformation and Weierstrass Elliptic Function Solutions of the Generalized (2+1)-Dimensional Coupled Davey-Stewartson Equation in Shallow Water Waves

This paper investigates the generalized (2+1)-dimensional coupled Davey-Stewartson (DS) equation, which describes the motions of long and short waves in shallow waters and has extensive applications in plasma physics. First, we study the Weierstrass elliptic function solutions using the auxiliary function method. Then, the bilinear Bäcklund transformation (BT) and Bell polynomial Bäcklund transformation are constructed using Bell polynomial method. Moreover, explicit 1-soliton, explicit 2-soliton, and explicit 3-soliton solutions are obtained from the derived bilinear form. Finally, the physical behaviors of the solutions are illustrated through three-dimensional plots, density plots, and two-dimensional planar graphs.