The Korteweg-de Vries (KdV) equation is derived from Landau two-fluid hydrodynamics applied to the thickness oscillation of the superfluid 4He film at low temperatures, where the main restoring force is van der Waals attraction from the substrate and the thermomechanical force due to phonons is a small correction. Since the usual third-sound generators and detectors are far wider than the individual solitons, the asymptotic solution of the KdV equation provided by the inverse scattering method is coarse-grained by regarding it as a continuous train of sharp pulses. The envelope so obtained still shows a singular front proportional to (t-t0)-1/2, where t0 is the arrival time of the fastest soliton, and should therefore be observable with the appropriate experimental arrangement.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)