The Peregrine breather on the zero-background limit as the two-soliton degenerate solution : an experimental study

Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrödinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.

Schlagworte

degenerate soliton

Peregrine breather on the zero-background limit

rogue waves

nonlinear waves

wave hydrodynamics

DDC Class

530: Physik

600: Technik

620: Ingenieurwissenschaften

Projekt(e)

EUR EIPHI ANR-17-EURE-0002 "Breathing Light" Project

PIA2/ISITE-BFC, ANR-15- IDEX-03 "Nextlight" Project

ANR-20-CE30-0004 Optimized on-demand ultrafast and broadband light sources using machine learning – OPTIMAL

Funding Organisations

Laboratory of Dynamical Systems and Applications NRU HSE, of the Ministry of Science and Higher Education of the Russian Federation

Russian Foundation for Basic Research

French National Research Agency

European Research Council

More Funding Information

AS was partially supported by Laboratory of Dynamical Systems and Applications NRU HSE, of the Ministry of Science and
Higher Education of the Russian Federation Grant 075-15-2019-1931; and by the Grant 21-55-15008 of the Russian Foundation for Basic Research. BK and JD acknowledge support from the French National Research Agency (EUR EIPHI ANR-17-EURE-0002 and PIA2/ISITE-BFC, ANR-15-IDEX-03, “Breathing Light” and “Nextlight” projects, and ANR-20-CE30-0004 “OPTIMAL” project). FD acknowledges support from the European Research Council (ERC-2018-AdG 833125 HIGHWAVE).

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https://creativecommons.org/licenses/by/4.0/

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The Peregrine breather on the zero-background limit as the two-soliton degenerate solution : an experimental study