Soliton-like solutions and other wave patterns in the nonlocal model of structured media

A set of invariant (travelling wave) solutions of a modelling system describing strong pulse loading afteraction in medium with internal structure is considered. Using the well known symmetry reduction method we perform the transition from the initial system of PDE to a third-order dynamical system. Employing the qualitative theory methods as well as direct numerical simulation, we study the appearance of multiperiodic, quasiperiodic, chaotic and soliton-like invariant solutions. Parametric portraits are presented and the structure of a set of parameter values, corresponding to the soliton-like solutions, is analyzed. Within the method applied this set manifests fractal features.