  We study the infinite time dynamics of a class of nonlinear Schr\"odinger /
Gross-Pitaevskii equations. In our previous paper, we prove the asymptotic
stability of the nonlinear ground state in a general situation which admits
degenerate neutral modes of arbitrary finite multiplicity, a typical situation
in systems with symmetry. Neutral modes correspond to purely imaginary
(neutrally stable) point spectrum of the linearization of the Hamiltonian PDE
about a critical point. In particular, a small perturbation of the nonlinear
ground state, which typically excites such neutral modes and radiation, will
evolve toward an asymptotic nonlinear ground state soliton plus decaying
neutral modes plus decaying radiation. In the present article, we give a much
more detailed, in fact quantitative, picture of the asymptotic evolution.
Specificially we prove an equipartition law: The asymptotic soliton which
emerges has a mass which is equal to the initial soliton mass plus one half the
mass contained in the initially perturbing neutral modes.
