The propagation of plane longitudinal waves in an infinite medium with point defects located in a non-stationary inhomogeneous temperature field is studied. A self-consistent problem is considered, taking into account both the influence of an acoustic wave on the formation and movement of defects, and the influence of defects on the propagation features of an acoustic wave. It is shown that in the absence of heat diffusion, the system of equations reduces to a nonlinear evolution equation with respect to the displacements of the particles of the medium. The equation can be considered a formal generalization of the Korteweg-de Vries-Burgers equation. By the method of truncated decompositions, an exact solution of the evolution equation in the form of a stationary shock wave with a monotonic decrease has been found. It is noted that dissipative effects due to the presence of defects prevail over the dispersion associated with the migration of defects in the medium.

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