On the Existence of Localized Invariant Solutions in  Relaxing Hydrodynamics Models

V.Vladimirov (Faculty of Applied Mathematics, University of Mining and Metallurgy, Cracow, Poland); S.I.Skurativskyy (Division of Geodynamics of Explosion, S.I. Subbotin Institute of Geophysics, NAS of Ukraine, Kiev, Ukraine)

e-mail: vsan@rambler.ru;vladimir@mat.agh.edu.pl

We consider a set of invariant travelling wave (TW) solutions for two modelling systems,  simulating long non-linear waves propagation in structured media. Using the methods of  local non-linear analysis and numerical simulation, we show that in both cases the set of  TW solutions contains localized soliton-like regimes, corresponding to homoclinic loops  of three-dimensional dynamical systems obtained from the initial systems of PDE through  the group theory reduction. We also show that a set of parameter vaues corresponding to  the homoclinic loops appearance looks like a smooth curve in the case of the first, more  simple modeling system, while the set corresponding to second system has a fractal structure


Section : 12