2013/12/31 by Alla Yurova · 3 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Generalization #Nonlinear Waves and Solitons #Nonlinear system #Ocean Waves and Remote Sensing #Protein filament #Soliton #Surface (topology) #Vortex #nlin.PS
paper · pdf · doi:10.1142/s0219887814500571
published in International Journal of Geometric Methods in Modern Physics 11(06), 1450057 (World Scientific) · 10 pages. Fixed typos, expanded and revised Sections II and III. Added the Conclusion and Acknowledgment. Added the new references
arxiv created 2014/01/19 · openalex publication_date 2014/03/20 · arxiv updated 2014/06/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Although the Peregrine-type solutions of the nonlinear Schrödinger (NLS) 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 paper 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 — the so-called exultons — of the NLS 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.