Abstract
Large amplitude, multiphase solutions of periodic discrete nonlinear Schrödinger (NLS) systems are excited and controlled by starting from zero and using a small perturbation. The approach involves successive formation of phases in the solution by driving the system with small amplitude plane wavelike perturbations (drives) with chirped frequencies, slowly passing through a system's resonant frequency. The system is captured into resonance and enters a continuing phase-locking (autoresonance) stage, if the drive's amplitude surpasses a certain sharp threshold value. This phase-locked solution is efficiently controlled by variation of an external parameter (driving frequency). Numerical examples of excitation of multiphase waves and periodic discrete breathers by using this approach for integrable (Ablowitz-Ladik) and nonintegrable NLS discretizations are presented. The excited multiphase waveforms are analyzed via the spectral theory of the inverse scattering method applied to both the integrable and nonintegrable systems. A theory of autoresonant excitation of 0- and 1-phase solutions by passage through resonances is developed. The threshold phenomenon in these cases is analyzed.
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