  Two different methods are proposed for the generation of wide classes of
exact solutions to the stationary Gross - Pitaevskii equation (GPE). The first
method, suggested by the work by Kondrat'ev and Miller (1966), applies to
one-dimensional (1D) GPE. It is based on the similarity between the GPE and the
integrable Gardner equation, all solutions of the latter equation (both
stationary and nonstationary ones) generating exact solutions to the GPE, with
the potential function proportional to the corresponding solutions. The second
method is based on the "inverse problem" for the GPE, i.e. construction of a
potential function which provides a desirable solution to the equation.
Systematic results are presented for 1D and 2D cases. Both methods are
illustrated by a variety of localized solutions, including solitary vortices,
for both attractive and repulsive nonlinearity in the GPE. The stability of the
1D solutions is tested by direct simulations of the time-dependent GPE.
