On the invariant soliton-like solutions of a non-integrable evolutionary system

Abstract:
We considered a modeling system, describing long nonlinear waves propagation in a medium, possessing an internal structure on mesoscale, and manifesting non-local features. The system occurs to be similar to some Hamiltonian system, but does no coincide with it for any physically justified values of the parameters. However a system of ODE's, obtained from the initial one via the self-similarity reduction occurs to be Hamiltonian. Using this fact, we show that the factorized system possesses a one-parameter family of homoclinic regimes, corresponding to soliton-like traveling wave solutions of the initial  system.