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.

中文翻译：

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超流氦中有限尺寸声子束的演化

考虑了高能和低能声子各向异性光束演化的非线性阶段。光束是相互作用的系统，在相空间中实际上是一维的。这些系统的空间和时间演化的观察和理论方法在一般情况下进行分析，当它们在纵向和横向方向上都有界时。结果，梁参数的方程组被简化为描述梁的纵向和横向演化的单个非线性方程。该方程的数值解解释了实验观察到的梁运动和变形的特征；它还可以确定梁的主要参数和演化阶段。