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Self-oscillations in ring Toda chains with negative friction.
W Ebeling1, P S Landa, V G Ushakov
1Institute of Physics, Humboldt-University Berlin, 10115 Berlin, Germany.
Summary
We investigated self-oscillation modes in ring Toda chains with negative friction. Two modes involve whole-chain rotation, while N-1 modes combine solitonlike behavior with mode-dependent rotation.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Soliton theory
Background:
- Toda chains exhibit complex dynamics under external influences.
- Negative friction can induce self-oscillations in discrete systems.
- Solitonlike solutions are characteristic of integrable systems like the Toda chain.
Purpose of the Study:
- To analyze the distinct modes of self-oscillation in ring Toda chains with Rayleigh-type negative friction.
- To characterize the behavior of these self-oscillations, particularly their relation to solitonlike solutions.
Main Methods:
- Analytical investigation of self-oscillation modes.
- Numerical simulations to complement analytical findings.
- Explicit calculation of oscillation modes for a Toda chain with N elements.
Main Results:
- Identified N+1 distinct modes of self-oscillation.
- Two modes correspond to uniform left/right rotation of the entire chain.
- N-1 modes exhibit a combination of solitonlike oscillations and mode-dependent rotation.
Conclusions:
- The study elucidates the diverse self-oscillation behaviors in dissipative Toda chains.
- A comprehensive classification of N+1 oscillation modes was achieved.
- Specific modes demonstrate unique rotational properties, including zero average velocity for antiphase oscillations in even N systems.