Vladimirov V.¹, Sapa L.¹, Skurativskyi S.² (¹AGH University of Science and Technology, Kraków, Poland; ²Subbotin Institute of Geophysics of NAS of Ukraine, Kyiv)

Influence of a choice of state equation describing heterogeneous media on the existence and stability of solitary wave self-similar solutions supported by the hydrodynamic-type model

Abstract: In this report a hierarchy of descriptions of the equation of state of a medium with an internal structure is considered. The state equation, together with the balance of mass and momentum equations form a closed system, which is used to describe propagation of waves in heterogeneous media. A model of this type with the lowest possible non-local description of the equation of state has been extensively studied in previous years. As part of these studies, the existence of soliton-like solutions describing waves of compression and rarefaction is strictly proven, and the types of stability of individual solutions are determined. Now we touch upon the problem of the existence of soliton-like traveling wave solutions in the analogous model closed by an equation of state standing at a higher level in the hierarchy of descriptions, as well as the problem of the stability of the localized solutions in question.