Elastic Waves in a Thermoelastic Medium with Point Defects

The propagation of plane longitudinal waves in an infinite medium with point defects has been investigated. The medium is assumed to be placed in a nonstationary nonuniform temperature field. A self-consistent problem considering both the influence of the acoustic wave on the generation and displacement of point defects and, conversely, the influence of point defects on the propagation of the acoustic wave has been considered. It has been shown that in the absence of heat diffusion, the corresponding set of equations reduces to a nonlinear evolutionary equation in particle displacements in the medium. This equation can be viewed as a formal generalization of the Korteweg-de Vries-Burgers equation. Using the finite difference method, an exact solution to the evolutionary equation in the form of a monotonically decreasing stationary shock wave has been found. It has been noted that defect-induced dissipation dominates over dispersion due to defect migration.