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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

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Solitonic Dispersive Hydrodynamics: Theory and Observation.

Michelle D Maiden¹, Dalton V Anderson¹, Nevil A Franco¹

¹Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA.

Physical Review Letters

|April 26, 2018

Summary

A new theory unifies solitons and dispersive hydrodynamics, revealing universal laws for nonlinear wave interactions. This predicts how solitons behave in fluid flows, with experiments confirming the findings.

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Area of Science:

Physics
Fluid Dynamics
Nonlinear Wave Phenomena

Background:

Nonlinear waves, including solitons and dispersive shock waves, are prevalent in various physical systems.
Existing research often studies solitons and dispersive hydrodynamics separately, lacking a unified theoretical framework and experimental validation.
Understanding their interactions is crucial for diverse fields like nonlinear optics and fluid mechanics.

Purpose of the Study:

To introduce a general soliton-mean field theory for describing soliton propagation in macroscopic hydrodynamic flows.
To identify universal adiabatic invariants governing soliton-hydrodynamic interactions.
To experimentally validate the developed theory and explore its broader implications.

Main Methods:

Development of a general soliton-mean field theory.
Identification of two universal adiabatic invariants of motion.
Experimental investigation using viscous fluid conduits to test theoretical predictions.

Main Results:

The theory successfully describes soliton propagation in hydrodynamic flows.
Two universal adiabatic invariants predict whether solitons are trapped or transmitted by hydrodynamic states.
Hydrodynamic reciprocity observed: solitons behave identically when encountering expansion waves or dispersive shock waves.
Experimental results quantitatively confirm the soliton-mean field theory.

Conclusions:

The developed soliton-mean field theory provides a unified framework for understanding soliton and dispersive hydrodynamic interactions.
The identified adiabatic invariants offer predictive power for soliton behavior in complex flows.
The findings have broad implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive media.