Gasdynamic Elements of Dispersive Medium

This work presents aspects of motion theory of the gaseous continuous medium at essential influence of dispersion effects, related to the medium microstructure or to the presence of own force fields of an electromagnetic or gravitational nature. The exact stationary solutions of non-linear equations in vicinity of transition fronts and in the shape of solitary waves – “classical” and “particle-like” solitons are analyzed in details. We demonstrate capabilities of building various gasdynamic models – starting with acoustic theory of relativity and supercritical analogue of the special theory of relativity up to model of the Newtonian dark matter and microstructural turbulence model. Common conformities of investigated processes are illustrated by a number of examples taken from gasdynamics and physics.