Reducing a generalized Davey–Stewartson system to a non-local nonlinear Schrödinger equation

In the present study, we consider a generalized (2 + 1) Davey–Stewartson (GDS) system consisting of a nonlinear Schrödinger (NLS) type equation for the complex amplitude of a short wave and two asymmetrically coupled linear wave equations for long waves propagating in an infinite elastic medium. We obtain integral representation of solutions to the coupled linear wave equations and reduce the GDS system to a NLS equation with non-local terms. Finally, we present localized solutions to the GDS system, decaying in both spatial coordinates, for a special choice of parameters by using the integral representation of solutions to the coupled linear wave equations.