Khasin M, Friedland L
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Dec;68(6 Pt 2):066214. doi: 10.1103/PhysRevE.68.066214. Epub 2003 Dec 31.
Large amplitude, multiphase excitations of the periodic Toda lattice (n-gap solutions) are created and controlled by small forcing. The approach uses passage through an ensemble of resonances and subsequent multiphase self-locking of the system with adiabatic wave-like perturbations. The synchronization of each phase in the excited lattice proceeds from the weakly nonlinear stage, where the problem can be reduced to that for a number of independent, driven, one-degree-of-freedom oscillatory systems. Due to this separability, the phase locking at this stage is robust, provided the amplitude of the corresponding forcing component exceeds a threshold, which scales as 3/4 power of the corresponding frequency chirp rate. The adiabatic synchronization continues into a fully nonlinear stage, as the driven lattice self-adjusts its state to remain in a persisting and stable multifrequency resonance with the driving perturbation. Thus, a complete control of the n-gap state becomes possible by slow variation of external parameters.
通过小的外力作用，可以产生并控制周期托达晶格的大幅度多相激发（n-隙解）。该方法利用了通过一系列共振以及随后系统与绝热波状扰动的多相自锁。受激晶格中各相位的同步从弱非线性阶段开始，在这个阶段，问题可以简化为多个独立的、受驱动的单自由度振荡系统的问题。由于这种可分离性，只要相应外力分量的幅度超过一个阈值，该阶段的锁相就是稳健的，该阈值与相应频率啁啾率的3/4次方成正比。随着受驱动晶格自我调整其状态，以与驱动扰动保持持续且稳定的多频共振，绝热同步会持续到完全非线性阶段。因此，通过缓慢改变外部参数，可以实现对n-隙状态的完全控制。
