An autoresonant approach for the excitation and control of one- and two-phase waves of a weakly nonlinear Klein-Gordon equation is proposed. It employs chirped-frequency driving waves passing through linear resonances in the system. Under certain conditions, the excited wave phase-locks to the drives, and its amplitude increases to maintain resonance as the wave enters the nonlinear stage. In the single-phase autoresonance, a slow-varying, growing-amplitude traveling wave emerges. Two-wave autoresonance leads to the formation of phase-locked space-time quasicrystals. The theory is based on Whitham's averaged variational approach and is supported by fully nonlinear simulations. It describes different autoresonant scenarios depending on the parameters in the system. Furthermore, the theory establishes threshold values of the driving amplitudes required for autoresonant excitation.

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• Lagrangian dynamics
• Synchronization