On a structure of the explicit solutions to the Davey-Stewartson equations

A general representation of explicit solutions to the Davey-Stewartson (DS) equations is obtained within the framework of the dressing method. The structure of the solutions with nonzero boundary values at infinity is established to coincide with the functional structure of the solutions to equations of the generalized KP hierarchy. The exponential and rational-type solutions are found both for the DS equations and for their one-dimensional reduction, the nonlinear Schrödinger equation.