Abstract |

**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