Double points of the slowness surface of the system of crystal acoustics for tetragonal crystals (Q357449)

In crystal acoustics it is essential to have a good understanding of the long-time behavior of the global solutions of the corresponding system of time-dependent second-order partial differential equations. In this paper, the author studies the case of tetragonal symmetry and relates his results to well-known results in cubic and hexagonal symmetries. One can obtain information (such as decay estimates) about the solutions of the Cauchy problem associated to the system of crystal acoustics from their representation as parametric integrals. Since these integrals live on the slowness surface, it is the aim of this paper to study singularities of this characteristic surface. In the case of tetragonal symmetry, the author studies the position and some geometric properties (with respect to the natural configuration of the given symmetry) of the double points of the slowness surface of the system of crystal acoustics.