Prediction and manipulation of hydrodynamic rogue waves via nonlinear spectral engineering

A. Tikan1, F. Bonnefoy2, G. Roberti3, G. El3, A. Tovbis4, G. Ducrozet2, A. Cazaubiel5, G. Prabhudesai6, G. Michel7, F. Copie1, E. Falcon5, S. Randoux1, and P. Suret1

1Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
2Ecole Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France
3Northumbria University, Dpt of Math., Newcastle upon Tyne, NE1 8ST, United Kingdom
4University of Central Florida, Dpt Math., Orlando, Florida, 32816, USA
5Université de Paris, MSC Laboratory, UMR 7057 CNRS, F-75 013 Paris, France
6LP, ENS, CNRS, Univ. Pierre et Marie Curie, Univ. de Paris, F-75 005 Paris, France
7Institut Jean Le Rond d'Alembert, Sorbonne Université, CNRS, UMR 7190, F-75 005 Paris, France


Reference: Physical Review Fluids 7, 054401 (2022)     Editor's
                                                          suggestion

URL:  https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.054401
DOI:  https://doi.org/10.1103/PhysRevFluids.7.054401

Abstract: Peregrine soliton (PS) is widely regarded as a prototype nonlinear structure capturing properties of rogue waves that emerge in the nonlinear propagation of unidirectional wave trains. As an exact breather solution of the one-dimensional focusing nonlinear Schrödinger equation with nonzero boundary conditions, the PS can be viewed as a soliton on finite background, i.e., nonlinear superposition of a soliton and a monochromatic wave. A recent mathematical work showed that both nonzero boundary conditions and solitonic content are not pre-requisites for the PS occurrence. Instead, it has been demonstrated that PS can emerge locally, as an asymptotic structure arising from the propagation of an arbitrary large decaying pulse, independently of its solitonic content. This mathematical discovery has changed the widely accepted paradigm of the solitonic nature of rogue waves by enabling the PS to emerge from a partially radiative or even completely solitonless initial data. In this work, we realize the mathematically predicted universal mechanism of the local PS emergence in a water tank experiment with a particular aim to control the point of the PS occurrence in space-time by imposing an appropriately chosen initial chirp. By employing the inverse scattering transform for the synthesis of the initial data, we are able to engineer a localized wave packet with a prescribed solitonic and radiative content. This enabled us to control the position of the emergence of the rogue wave by adjusting the inverse scattering spectrum. The proposed method of the nonlinear spectral engineering is found to be robust to higher-order nonlinear effects inevitable in realistic wave propagation conditions.

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