title: Unsteady evolution of localized unidirectional deep-water wave groups.
abstract: We study the evolution of localized wave groups in unidirectional water wave envelope equations [the nonlinear Schrödinger (NLSE) and the modified NLSE (MNLSE)]. These localizations of energy can lead to disastrous extreme responses (rogue waves). We analytically quantify the role of such spatial localization, introducing a technique to reduce the underlying partial differential equation dynamics to a simple ordinary differential equation for the wave packet amplitude. We use this reduced model to show how the scale-invariant symmetries of the NLSE break down when the additional terms in the MNLSE are included, inducing a critical scale for the occurrence of extreme waves.
authors.affiliation: Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02142, USA.
authors.forename: Will
authors.initials: W
authors.lastname: Cousins
authors.affiliation: Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02142, USA.
authors.forename: Themistoklis P
authors.initials: TP
authors.lastname: Sapsis