Evolution of finite-size phonon beams in superfluid helium
R.V. Vovk and K.E. Nemchenko
V.N. Karazin Kharkiv National University, 4 Svobody Square, Kharkiv 61022, Ukraine
Received December 12, 2019, published online March 24, 2020
The nonlinear stage of the evolution of anisotropic beams of high-energy and low-energy phonons, which are practically one-dimensional interacting systems in phase space, is considered in the work. The analysis of the results of observations and theoretical consideration of the spatial and temporal evolution of these systems in the general case, when they are limited in the longitudinal and transverse directions, are carried out. As a result of the work, the system of equations for the beam parameters is reduced to a single nonlinear equation that describes the longitudinal and transverse evolution of the beam. A numerical solution of this equation made it possible to explain the characteristic features of the motion and deformation of the beams that are observed experimentally, as well as to determine the main parameters and stages of the evolution of the beams.
Key words:  superfluid helium, phonon propagation, phonon beam, heat pulses.