Soliton dynamics for the nonlinear Schr\"odinger equation with magnetic field

The semiclassical limit of a nonlinear focusing Schr"odinger equation in presence of nonconstant electric and magnetic potentials V,A is studied by taking as initial datum the ground state solution of an associated autonomous elliptic equation. The concentration curve of the solutions is a parameterization of the solutions of a Newton ODE involving the electric force as well as the magnetic force via the Lorenz law of electrodynamics.