Abstract
This paper presents a physical model described by the (2 +1)-dimensional nonlinear Schrodinger equation with variable coefficients (2D-VcNLSE). The 2D-VcNLSE is related to many physical phenomena in nonlinear optical fibers, Bose-Einstein condensates, and water waves. We study new types of nonautonomous complex wave solutions in the presence of inhomogeneous media. Various structures of these solutions such as bright and dark soliton and similarity solutions are investigated. Furthermore, different exact solutions for the 2D-VcNLSE are obtained via the G'/G-expansion method. Through 3D- and contour plots, we show that the dynamical behaviors of the obtained solutions can be effectively controlled by modulating the values of the arbitrary functions in these solutions.