Mach disks and caustic reflections, caustics, application to astrophysics

An important part of a special set is caustic. Dynamically, the body of a certain shape seeks to change its shape to the caustic of this form (in the absence or disparaging small forces of interaction). This explains the evolution of Elliptical (ellipsoid-shaped) galaxies, as younger ones, to Spiral and to Spiral with a jumper (Spiral barred) galaxies. It also explains the existence of galaxies with a polar ring. In short, caustics is the law of evolution of forms. It should be noted that the idea of forms of galaxies as caustics, generated by gravitational waves, belongs to Ya. B. Zeldovich.
We will consider stable structures (the reflection caustics) in the dynamical process of reflection of waves, which, in our opinion, are nothing else than the well-known Mach disks (rhombuses, or diamonds). We construct models in which the medium internal velocity and/or its distribution inside the medium is allowed.
The reflection law underlying the construction of the corresponding models was put forward in paper ( I. G. Tsar'kov Smooth solutions of the eikonal equation and the behavior of local minima of the distance function. Izv. Math. 2019.V. 83 (6). P. 1234—1258).
We will consider a domain whose boundary separates two media. In this case, a special position of boundary points generates excitation waves, which when passing through the domain have multiple reflections from its boundary inside this domain.
We will study the caustic of this process, i.e., the spot of matter compression inside the domain (usually, in the case of gases) or of pressure elevation (usually, for liquids).
We will give an algorithm for construction of such a set, which will be called the reflection caustic.
As examples of such sets, we mention the Mach disks, which appear in various natural phenomena:
plasma plumes of jet-propelled engines, jets of water downstream pipes or water taps, rock avalanches, and in many other natural and anthropogenic phenomena.