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Emergence and control of multiphase nonlinear waves by synchronization.
1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Physical Review Letters
|March 14, 2003
Summary
A small forcing can control large amplitude waves in the periodic Korteweg-de Vries equation by exciting resonances. Phase synchronization is robust if the driving amplitude surpasses a specific threshold.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
- Wave Phenomena
Background:
- The periodic Korteweg-de Vries equation models complex wave behaviors.
- Controlling large amplitude multiphase solutions presents significant challenges.
Purpose of the Study:
- To investigate methods for exciting and controlling large amplitude multiphase solutions.
- To analyze the synchronization mechanisms of these wave solutions.
Main Methods:
- Utilizing a small external forcing to perturb the system.
- Employing passage through an ensemble of resonances.
- Applying multiphase self-locking with eikonal-type perturbations.
Main Results:
- Demonstrated successful excitation and control of large amplitude multiphase solutions.
- Identified resonance passage as a key mechanism for control.
- Showcased robust phase synchronization of Korteweg-de Vries waves.
Conclusions:
- Small forcing can effectively control complex wave dynamics.
- Phase synchronization is achievable and robust above a critical driving amplitude threshold.