Temporal Fourier spectra of stationary and slowly moving breathers in Fermi–Pasta–Ulam anharmonic lattice

The temporal Fourier spectra of stationary and slowly moving self-localized large-amplitude modes (breathers) in translationally invariant chain of coupled classical anharmonic oscillators are studied. The breathers arise naturally in the anharmonic lattice from modulational instability of short-wavelength extended vibrational modes. The frequencies of the resonant spectral peaks of the stationary breather are measured numerically and compared with an exact analytical solution for the stationary extended nonlinear sinusoidal wave in the anharmonic lattice, which is conveniently adapted. Symmetrical satellite peaks of the fundamental frequency and its higher odd harmonics in the temporal Fourier spectrum of the stationary breather are observed. Small admixture of the slowly moving breather solution to the stationary one is discussed in connection with these peaks. It is observed that the temporal Fourier spectrum of slowly moving breather consists of two main frequencies symmetrically shifted upwards and downwards with respect to the fundamental frequency of the stationary breather with the same energy, in perfect agreement with the earlier theoretical prediction of one of the authors. The relation between the group velocity of slowly moving breather and the fundamental frequency of the stationary breather with the same energy is derived.