  We study the evolution of localized wave groups in unidirectional water wave
envelope equations (nonlinear Schrodinger (NLS) and modified NLS (MNLS)). These
localizations of energy can lead to disastrous extreme responses (rogue waves).
Previous studies have focused on the role of energy distribution in the
frequency domain in the formation of extreme waves. We analytically quantify
the role of spatial localization, introducing a novel technique to reduce the
underlying PDE dynamics to a simple ODE for the wave packet amplitude. We use
this reduced model to show how the scale- invariant symmetries of NLS break
down when the additional terms in MNLS are included, inducing a critical scale
for the occurrence of extreme waves.
