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

TL;DR

This paper experimentally investigates the degenerate two-soliton solution, a zero-background counterpart to the Peregrine breather, demonstrating wave amplification factors consistent with nonlinear Schrödinger equation predictions in water wave experiments.

Contribution

It provides experimental evidence and numerical analysis of the degenerate two-soliton solution on zero background in hydrodynamics, expanding understanding of multi-soliton dynamics.

Findings

Wave amplification factor of two observed experimentally

Good agreement with nonlinear Schrödinger equation simulations

Physical limitations of degenerate two-solitons quantified

Abstract

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 Schr\"odinger 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.