  We study the existence and stability of localized states in the
two-dimensional (2D) nonlinear Schrodinger (NLS)/Gross-Pitaevskii equation with
a symmetric four-well potential. Using a fourmode approximation, we are able to
trace the parametric evolution of the trapped stationary modes, starting from
the corresponding linear limits, and thus derive the complete bifurcation
diagram for the families of these stationary modes. The predictions based on
the four-mode decomposition are found to be in good agreement with the
numerical results obtained from the NLS equation. Actually, the stability
properties coincide with those suggested by the corresponding discrete model in
the large-amplitude limit. The dynamics of the unstable modes is explored by
means of direct simulations. Finally, while we present the full analysis for
the case of the focusing nonlinearity, the bifurcation diagram for the
defocusing case is briefly considered too.
