UC Berkeley

Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situ-ations where the decay of solutions at infinity is borderline and scattering fails just barely. An interesting example is that of problems with cubic nonlineari-ties 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.