A hidden life of Peregrine's soliton: rouge waves in the oceanic depths

Abstract

Although the Peregrine-type solutions of the nonlinear Sch\"odinger equation have long been associated mainly with the infamous "rouge waves" on the surface of the ocean, they might have a much more interesting role in the oceanic depths; in this article we show that these solutions play an important role in the evolution of the intrathermocline eddies, also known as the "oceanic lenses". In particular, we show that the collapse of a lens is determined by the particular generalization of the Peregrine soliton -- so called exultons -- of the nonlinear Schr\"odinger equation. In addition, we introduce a new mathematical method of construction of a vortical filament (a frontal zone of a lens) from a known one by the Darboux transformation.