  Modified scattering phenomena are encountered in the study of global
properties for nonlinear dispersive partial differential equations in
situations where the decay of solutions at infinity is borderline and
scattering fails just barely. An interesting example is that of problems with
cubic nonlinearities in one space dimension.
  The method of testing by wave packets was introduced by the authors as a tool
to efficiently capture the asymptotic equations associated to such flows, and
thus establish the modified scattering mechanism in a simpler, more efficient
fashion, and at lower regularity. In these expository notes we describe how
this method can be applied to problems with general dispersion relations.
