Quasibreathers in MMT model

TL;DR

This paper reports the numerical discovery of quasibreathers, oscillating localized wave structures in the MMT model that resemble ocean freak waves and exhibit stable or oscillatory behaviors depending on amplitude.

Contribution

It introduces quasibreathers as a new type of localized solution in the MMT model, expanding understanding of nonlinear wave dynamics.

Findings

Quasibreathers resemble ocean freak wave groups.

Small amplitude quasibreathers are stable.

Large amplitude quasibreathers oscillate due to weak collapses.

Abstract

We report numerical detection of new type of localized structures in the frame of Majda-McLaughlin-Tabak (MMT) model adjusted for description of essentially nonlinear gravity waves on the surface of ideal deep water. These structures -- quasibreathers, or oscillating quasisolitons -- can be treated as groups of freak waves closely resembling experimentally observed "Three Sisters" wave packs on the ocean surface. The MMT model has quasisolitonic solutions. Unlike NLSE solitons, MMT quasisolitons are permanently backward radiating energy, but nevertheless do exist during thousands of carrier wave periods. Quasisolitons of small amplitude are regular and stable, but large-amplitude ones demonstrate oscillations of amplitude and spectral shape. This effect can be explained by periodic formation of weak collapses, carrying out negligibly small amount of energy. We call oscillating quasisolitons "quasibreathers".