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Multiphase control of a nonlinear lattice.

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.