Multiphase control of a nonlinear lattice

Large amplitude, multiphase excitations of the periodic Toda lattice [Formula presented]-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 wavelike 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.