  We develop the method of vector-fields to further study Dispersive Wave
Equations.
  Radial vector fields are used to get a-priori estimates such as the Morawetz
estimate on solutions of Dispersive Wave Equations.
  A key to such estimates is the repulsiveness or nontrapping conditions on the
flow corresponding to the wave equation. Thus this method is limited to
potential perturbations which are repulsive, that is the radial derivative
pointing away from the origin. In this work, we generalize this method to
include potentials which are repulsive relative to a line in space (in three or
higher dimensions), among other cases. This method is based on constructing
multi-centered vector fields as multipliers, cancellation lemmas and energy
localization.
