We study the non-reflective propagation of kink waves in inhomogeneous magnetic-flux tubes. We use the thin-tube and zero-beta plasma approximations. The wave equation with the variable velocity is reduced to the Euler–Poisson–Darboux equation. This equation contains one dimensionless parameter. There are two infinite sequences of this parameter, one monotonically increasing and the other monotonically decreasing, when exact analytical solutions for the Euler–Poisson–Darboux equation can be obtained. For the monotonically increasing sequences the Euler–Poisson–Darboux equation becomes the equation describing spherically symmetric waves in multi-dimensional spaces. The general results are applied to kink-wave propagation in coronal magnetic loops. We consider a coronal magnetic loop of a half-circular shape. We find that for a fixed loop height there is a one-parametric family of dependences of the loop cross-sectional radius on the coordinate along the loop corresponding to the non-reflective kink-wave propagation.

我们研究了非均匀磁通管中扭结波的非反射传播。我们使用细管和零β等离子体近似。速度可变的波动方程简化为欧拉-泊松-达布方程。该方程包含一个无量纲参数。当可以获得 Euler-Poisson-Darboux 方程的精确解析解时，该参数有两个无限序列，一个单调递增，另一个单调递减。对于单调递增序列，欧拉-泊松-达布方程成为描述多维空间中球对称波的方程。一般结果适用于日冕磁环中的扭结波传播。我们考虑半圆形的日冕磁环。我们发现，对于固定的环路高度，环路横截面半径与沿环路的坐标（对应于非反射扭结波传播）存在一参数依赖性。