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Dissipative double-well potential: nonlinear stationary and pulsating modes.
Dmitry A Zezyulin1, Vladimir V Konotop, Georgy L Alfimov
1Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal. zezyulin@cii.fc.ul.pt
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
Researchers analyzed nonlinear modes in a double-well potential. Stable modes, including nonsymmetric ones, were found with repulsive nonlinearity, unlike attractive nonlinearity where no stable modes exist.
Area of Science:
- Nonlinear dynamics
- Complex systems physics
- Optical systems
Background:
- Double-well potentials are fundamental in various physical systems.
- Understanding nonlinear modes is crucial for predicting system behavior.
- Gain media introduce unique dynamics to potential landscapes.
Purpose of the Study:
- To analyze nonlinear modes in a complex absorbing double-well potential with linear gain.
- To investigate the existence and stability of these modes under different nonlinearity conditions.
- To explore the dynamic transitions between modes.
Main Methods:
- Numerical analysis using a modified "shooting" method.
- Investigation of nonlinear mode families and their bifurcations.
- Linear stability analysis and dynamic simulations.
Main Results:
- No stable nonlinear modes were found for attractive nonlinearity.
- Stable nonlinear modes, including nonsymmetric ones, were identified for repulsive nonlinearity.
- Control parameter variations induced switching between different modes.
- Pulsating solutions emerged from unstable modes.
Conclusions:
- Repulsive nonlinearity is key for stable nonlinear modes in this system.
- System dynamics are highly sensitive to control parameters, allowing mode switching.
- The study reveals complex behaviors including stable, nonsymmetric, and pulsating modes.
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