Velocity of the traveling intrinsic localized mode in the real self-dual nonlinear network lattice: Experiments and analysis

抄録

In the self-dual nonlinear network lattice, the intrinsic localized mode (ILM) travels almost freely because of its very weak interaction with linear phonon modes, even when the nonlinear lattice is not integrable. In experiments, a propagating wave driver is used in the ring-shaped lattice to maintain the traveling ILMs by compensating for the unavoidable energy loss due to damping. The amplitude and velocity increase with the driver frequency F because of the positive nonlinearity of the lattice. Small steps are observed in the velocity curve when it is plotted as a function of the driver frequency. Between adjacent steps, the ratio (velocity)/(driver frequency) remains nearly constant, which implies that synchronization between the rotational motion of the ILM in the ring and the ILM vibration occurs. Simulations reveal that the appearance of the steps requires a faster velocity scaling as F^a (a ＞ 1, typically ∼ 1.4). The large damping at zero voltage and zero current – so called saturable damping – produces this velocity-boosting effect. The Fourier amplitude on the dispersion line (DL) of the traveling ILM is analyzed, and the shift of the DL spectrum explains the enhanced velocity.