Dislocations of soliton lattices: experiment and theory

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].

Figures (5)

• Figure 1: (a)The motion of a bright breather along a cnoidal wave at different moments in time. The bottom panel corresponds to the unperturbed cnoidal wave. (b) The trajectory of a bright breather on the t-z plane (dashed red line) against a background of straight blue lines corresponding to the propagation of the cnoidal wave.
• Figure 2: Dark breather trajectory on the $t-z$ plane (light blue line) against the background of the cnoidal wave.
• Figure 3: (a) Scattering of two bright breathers. (c) Scattering of two dark breathers. (e) Scattering of a bright and dark breather.
• Figure 4: Band positions in the complex plane $a$.
• Figure 5: (a) Soliton in the form of a dislocation with parameters from the first band gap. (b) Soliton in the form of a dislocation with parameters from the second band gap. (c) Cnoidal wave.