A hidden life of Peregrine's soliton: rouge waves in the oceanic depths
arXiv:1312.6900 · doi:10.1142/S0219887814500571
Abstract
Although the Peregrine-type solutions of the nonlinear Schödinger 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 Schrödinger 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.
arXiv comment10 pages. Fixed typos, expanded and revised Sections II and III. Added the Conclusion and Acknowledgment. Added the new references