Polуnomial solutions of nonlinear system of PDE describing dynamics of complex medium with oscillating inclusions

Abstract

The paper considers polуnomial solutions to a nonlinear system of PDE describing dynamics of complex medium with oscillating inclusions. In particular, it is shown that the coefficients of leading monomials satisfy a strongly nonlinear dynamical system of Hamiltonian type. This system may have periodic, quasiperiodic, and chaotic regimes when the model's control parameter is varied. The observed regimes were studied by means of analysis of Poincare sections and spectra of Lyapunov exponents.