  In this paper, we consider the long time dynamics of radially symmetric
solutions of nonlinear Schr\"odinger equations (NLS) having a minimal mass
ground state. In particular, we show that there exist solutions with initial
data near the minimal mass ground state that oscillate for long time. More
precisely, we introduce a coordinate defined near the minimal mass ground state
which consists of finite and infinite dimensional part associated to the
discrete and continuous part of the linearized operator. Then, we show that the
finite dimensional part, two dimensional, approximately obeys Newton's equation
of motion for a particle in an anharmonic potential well. Showing that the
infinite dimensional part is well separated from the finite dimensional part,
we will have long time oscillation.
