Quasibreathers in the MMT model

Abstract

We report numerical detection of a 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 packets 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”.