The global bifurcation picture for ground states in nonlinear Schrodinger equations

In this paper, we propose a method of finding all coherent structures supported by a given nonlinear wave equation. It relies on enhancing the recent global bifurcation theory as developed by Dancer, Toland, Buffoni and others, by determining all the limit points of the coherent structure manifolds at the boundary of the Fredholm domain. Local bifurcation theory is then used to trace back these manifolds from their limit points into the interior of the Fredholm domain identifying the singularities along them. This way all coherent structure manifold are discovered except may be the ones which form loops and hence never reach the boundary. The method is then applied to the Schrodinger equation with a power nonlinearity for which all ground states are identified.