Instability of symmetric stationary states for some nonlinear Schroedinger equations with an external magnetic field

This work is concerned with instability properties of solutions u(t,x)=e-iωΦ(x) of the Schroedinger equation in the presence of a uniform magnetic field, defined by a solenoidal vector potential Φ is a solution of the nonlinear elliptic equation, invariant by rotations around the z-axis, and solving a certain variational problem. We prove that Σ is unstable by the flow of the evolution equation. Moreover, the trajectories used to exhibit instability are global and uniformly bounded