Akademia Gorniczo-Hutnicza  im. Stanislawa Staszica
Wydzial Watematyki Stosowanej
Aleja Mickiewicha 30
30-059 Krakow POLAND

E-mail:  vladimir@mat.agh.edu.pl

On the existence of soliton-like invariant solutions of non-integrable hyperbolic-type system

Abstract:
We consider a modelling system of PDE, describing media with internal structure. Hydrodynamic-type equation of motion forms the closed system  when being considered together   with the kinetic  equation, attributed to the processes of energy release on the microlevel. A set of travelling wave invariant solutions is studied within the local non-linear analysis  methods,
that enable to formulate analytical conditions for the existence of homoclinic  loops, corresponding to  the solitary-wave solutions.  The results obtained are backed by the direct numerical simulation.