Nonlinear Schrödinger Equations with a Four-Well Potential in Two Dimensions: Bifurcations and Stability Analysis.

We report a full bifurcation diagram for trapped states in the two-dimensional (2D) nonlinear Schrödinger (NLS) equation with a symmetric four-well potential. Starting from the linear limit, we use a four-mode approximation to derive a system of ordinary differential equations, which makes it possible to trace the evolution of all trapped stationary modes, and thus to identify different branches of solutions bifurcating in the full NLS model. Their stability is examined within the framework of the linear stability analysis. [ABSTRACT FROM AUTHOR]