Evolution of finite-size phonon beams in superfluid helium

The nonlinear stage in the evolution of anisotropic beams of high-energy and low-energy phonons is considered. The beams are interacting systems that are virtually one-dimensional in phase space. The observations and theoretical approaches to the space and time evolution of these systems are analyzed in the general case, when they are bounded in both the longitudinal and transverse directions. As a result, the system of equations for the beam parameters is reduced to a single nonlinear equation that describes both the longitudinal and transverse evolution of the beam. The numerical solution of this equation provides an explanation of the experimentally observed characteristic features of the beam motion and deformation; it also enables the determination of the beams’ main parameters and stages of evolution.