RESUMEN
We study instabilities and relaxation to equilibrium in a long-range extension of the Fermi-Pasta-Ulam-Tsingou (FPU) oscillator chain by exciting initially the lowest Fourier mode. Localization in mode space is stronger for the long-range FPU model. This allows us to uncover the sporadic nature of instabilities, i.e., by varying initially the excitation amplitude of the lowest mode, which is the control parameter, instabilities occur in narrow amplitude intervals. Only for sufficiently large values of the amplitude, the system enters a permanently unstable regime. These findings also clarify the long-standing problem of the relaxation to equilibrium in the short-range FPU model. Because of the weaker localization in mode space of this latter model, the transfer of energy is retarded and relaxation occurs on a much longer timescale.
RESUMEN
The contributions of dipole-dipole interactions to the dynamics of solitons on a one-dimensional discrete easy-plane Heisenberg ferromagnet, in which the biquadratic exchange interactions are taken into account in addition to the Zeeman energy, the uniaxial anisotropy, and the exchange energy, are studied numerically. The results of a numerical simulation of the dynamics of a single soliton, as well as collision between a soliton-antisoliton pair, indicated that the energy-velocity curves for the solitons in the ferromagnetic chain present the signature of five different branches corresponding to different types of nonlinear elementary excitations in the chain.