Solitonic Dispersive Hydrodynamics: Theory and Observation

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.