  Based on our previous work for solving the nonlinear Schrodinger equation
with multichannel dynamics that is given by a localized standing wave and
radiation, in this work we deal with the multichannel solution which consists
of a moving soliton and radiation. We apply the modulation theory to give a
system of ODEs coupled to the radiation term for describing the solution, which
is valid for all times. The modulation equations are solved accurately by the
proposed numerical method. The soliton and radiation are captured separately in
the computation, and they are solved on the translated domain that is moving
with them. Thus for a fixed finite physical domain in the lab frame, the
multichannel solution can pass through the boundary naturally, which can not be
done by imposing any existing boundary conditions. We comment on the
differences of this method from the collective coordinates.
