Dislocations of soliton lattices: experiment and theory

TL;DR

This paper presents experimental observations of soliton lattice dislocations in fluid interfaces, confirming the 50-year-old KdV theory of cnoidal waves and their dislocations.

Contribution

It provides experimental validation of the KdV-based theory of soliton lattice dislocations in fluid systems.

Findings

Observation of two types of lattice dislocations with elastic interactions

Experimental confirmation of the KdV theory of cnoidal waves and dislocations

Visualization of soliton lattice behavior in cylindrical fluid channels

Abstract

The results of recent experiments [1] on observing soliton lattices and their dislocations in vertical cylindrical channels filled with immiscible fluids with strongly different viscosities and but slightly different densities are discussed. The less viscous, lower-density fluid fills the central region of the cylinder. Injecting a light fluid from below generates nonlinear cnoidal waves at the interface between the fluids, which have the appearance of soliton lattices. Two types of lattice dislocations are observed, the interaction between which is elastic. This experimental study fully confirms the theory of cnoidal waves and their dislocations for the KDV equation, which was developed 50 years ago and published in JETP [2].