Excitation of travelling multibreathers in anharmonic chains

Abstract

We study the dynamics of the "externally" forced and damped Fermi-Pasta-Ulam (FPU) 1D lattice. The forcing has the spatial symmetry of the Fourier mode with wavenumber p and oscillates sinusoidally in time with the frequency omega. When omega is in the phonon band, the p-mode becomes modulationally unstable above a critical forcing, which we determine analytically in terms of the parameters of the system. For omega above the phonon band, the instability of the p-mode leads to the formation of a travelling multibreather, that, in the low-amplitude limit could be described in terms of soliton solutions of a suitable driven-damped nonlinear Schroedinger (NLS) equation. Similar mechanisms of instability could show up in easy-axis magnetic structures, that are governed by such NLS equations.