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Extreme events in discrete nonlinear lattices
A Maluckov1, Lj Hadzievski, N Lazarides
1Faculty of Sciences and Mathematics, Department of Physics, P.O. Box 224, 18001 Nis, Serbia.
Summary
Statistical analysis of nonlinear waves in the Salerno model reveals power law amplitude distributions. Freak wave events are enhanced near the integrable limit due to soliton interactions and stochasticity.
Area of Science:
- Nonlinear dynamics
- Statistical physics
- Wave phenomena
Background:
- The Salerno model interpolates between integrable and nonintegrable discrete nonlinear equations.
- Discrete nonlinear waves can exhibit extreme events like rogue waves.
- Modulational instability is a key mechanism for wave amplitude growth.
Purpose of the Study:
- To statistically analyze extreme wave events in the Salerno model.
- To investigate the role of integrability and soliton interactions in freak wave formation.
- To understand the transition to stochasticity in discrete nonlinear systems.
Main Methods:
- Statistical analysis of discrete nonlinear waves.
- Investigation of the Salerno model, interpolating between the Ablowitz-Ladik (AL) equation and the discrete nonlinear Schrödinger equation.
- Monitoring stochasticity using the positive Lyapunov exponent.
Main Results:
- A power law dependence was found in the wave amplitude distribution.
- Freak wave probability is enhanced near the integrable limit of the Salerno model.
- A peak in extreme event probability is linked to discrete soliton interactions and a transition to global stochasticity.
Conclusions:
- The Salerno model exhibits power law statistics for wave amplitudes, with enhanced freak wave occurrences near integrability.
- Discrete soliton interactions play a crucial role in the onset of extreme events and system stochasticity.
- The study provides insights into the statistical behavior of nonlinear waves and extreme events in systems bridging integrable and nonintegrable regimes.
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