Solitonic dispersive hydrodynamics: theory and observation

TL;DR

This paper introduces a unified soliton-mean field theory to describe nonlinear wave interactions in dispersive media, experimentally confirming predictions about soliton behavior in hydrodynamic flows with broad scientific implications.

Contribution

It presents the first comprehensive theory linking solitons and dispersive hydrodynamics, supported by experimental validation in viscous fluid conduits.

Findings

Identification of two universal adiabatic invariants predicting soliton trapping or transmission.

Discovery of hydrodynamic reciprocity in soliton interactions with different wave structures.

Experimental confirmation of the theory in viscous fluid conduit experiments.

Abstract

Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.