The Burgers equation also describes a wide class of nonlinear effects arising in wave propagation theory, plasma physics, and acoustics. The Burgers type equation follows from the equations of the coupled nonlinear theory of thermoelasticity. In this paper it is shown that a generalization of the Burgers equation can be approached by constructing traveling wave type solutions in coupled models of solid-phase combustion. Examples of partial problems in which the automodel solution is a thermo-chemo-mechanical wave running with a uniform velocity are presented. They include a model considering only thermal expansion, a model considering concentration expansion; a generalization of the model for finite strains; and a model considering the dependence of the reaction velocity on the stress work. The wave velocity is determined by the method of jointed asymptotic expansions. A brief review of the author's works with the development of coupled models for practical applications to the synthesis of new materials and coatings; to different variants of surface treatment is presented.