Nonlinear dispersion relation in integrable turbulence

TL;DR

This paper measures the nonlinear dispersion relation in integrable turbulence of 1D deep water waves, revealing soliton presence and high-order effects, thus advancing understanding of nonlinear wave phenomena.

Contribution

It introduces an original method to accurately measure the NDR in integrable turbulence, emphasizing its significance in wave dynamics and soliton detection.

Findings

NDR characterized by frequency shift and broadening

Detection of solitons and high-order effects

Relevance of NDR in integrable turbulence

Abstract

The concept of Nonlinear dispersion relation (NDR) is used in various fields of Physics (nonlinear optics, hydrodynamics, hydroelasticity, mechanics, quantum optics, plasma physics,...) to characterize fundamental phenomena induced by nonlinearity such as wave frequency shift or turbulence. Nonlinear random waves described by the onedimensional nonlinear Schrodinger equation (1DNLSE) exhibit a remarkable form of turbulence called "integrable turbulence" where solitons play a key role. Surprisingly, little attention has been paid to the NDR of such universal wave systems up to a very recent theoretical study. Here, by using an original strategy, we report the accurate measurement of NDR of the slowly varying envelop of the waves in one-dimensional deep water waves experiments. We characterize precisely the frequency shift and the broadening of the NDR, which interestingly reveals the presence of solitons and of high order effects. Our results highlight the relevance of the NDR in the context of integrable turbulence.