Hydrodynamic Supercontinuum

TL;DR

This paper experimentally investigates multi-soliton solutions of the nonlinear Schrödinger equation in water waves, demonstrating phenomena like breather formation, wave focusing, and spectral broadening, with implications for understanding hydrodynamic supercontinuum generation.

Contribution

It provides the first detailed experimental observation of hydrodynamic supercontinuum and soliton fission in water waves, paralleling optical supercontinuum processes.

Findings

Good agreement between experiments and NLS predictions for low steepness waves

First controlled observation of hydrodynamic supercontinuum in water

Identification of soliton fission as a mechanism for spectral broadening

Abstract

We demonstrate experimentally multi-bound-soliton solutions of the Nonlinear Schr\"odinger equation (NLS) in the context of surface gravity waves. In particular, the Satsuma-Yajima N-soliton solution with N=2,3,4 is investigated in detail. Such solutions, also known as breathers on zero background, lead to periodic self-focussing in the wave group dynamics, and the consequent generation of a steep localized carrier wave underneath the group envelope. Our experimental results are compared with predictions from the NLS for low steepness initial conditions where wave-breaking does not occur, with very good agreement. We also show the first detailed experimental study of irreversible massive spectral broadening of the water wave spectrum, which we refer to by analogy with optics as the first controlled observation of hydrodynamic supercontinuum a process which is shown to be associated with the fission of the initial multi-soliton bound state into individual fundamental solitons similar to what has been observe in optics.