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Multiphase autoresonant excitations in discrete nonlinear Schrödinger systems
Y Gopher1, L Friedland, A G Shagalov
1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
Researchers excited large amplitude, multiphase solutions in discrete nonlinear Schrödinger (NLS) systems using chirped frequency drives. Autoresonance captures the system above a threshold, enabling efficient control of these complex wave solutions.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
- Wave Phenomena
Background:
- Discrete nonlinear Schrödinger (NLS) systems model various physical phenomena.
- Exciting and controlling large amplitude, multiphase solutions remains a challenge.
Purpose of the Study:
- To develop a method for exciting and controlling large amplitude, multiphase solutions in periodic discrete NLS systems.
- To investigate the phenomenon of autoresonance in these systems.
Main Methods:
- Utilizing small amplitude plane wavelike perturbations with chirped frequencies to drive the system.
- Slowly sweeping the driving frequency through a system's resonant frequency.
- Analyzing solutions using spectral theory and the inverse scattering method.
Main Results:
- Successful excitation of multiphase waves and discrete breathers in both integrable and nonintegrable NLS systems.
- Demonstration of autoresonance capture above a sharp amplitude threshold.
- Efficient control of phase-locked solutions by external parameter variation.
Conclusions:
- The proposed autoresonant driving method effectively excites and controls complex wave solutions in discrete NLS systems.
- A threshold phenomenon governs the capture into autoresonance.
- The spectral theory provides a framework for analyzing these solutions.