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Breathers in strongly anharmonic lattices
Philip Rosenau1, Arkady Pikovsky2
1School of Mathematics, Tel-Aviv University, Tel-Aviv 69978, Israel.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
Summary
We found stable, localized energy packets called finite amplitude breathers in an anharmonic Klein-Gordon lattice. These breathers exhibit unique behaviors near continuum and anticontinuum states, with stability depending on lattice spacing.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Lattice dynamics
Background:
- Anharmonic lattices support localized energy excitations.
- Klein-Gordon models describe discrete nonlinear systems.
- Breathers are stable, localized nonlinear waves.
Purpose of the Study:
- To investigate finite amplitude breathers in a specific anharmonic lattice.
- To analyze breather localization and stability.
- To compare numerical findings with theoretical models.
Main Methods:
- Direct numerical simulations of the lattice model.
- Derivation and application of a quasilinear Schrodinger equation (QLS).
- Analysis of breather localization rates and stability thresholds.
Main Results:
- Finite amplitude breathers are localized with doubly exponential decay rates.
- Breather behavior depends on proximity to continuum or anticontinuum states.
- A stability threshold for breathers was identified, improving with lattice sparseness.
Conclusions:
- The study characterizes novel breathers in anharmonic Klein-Gordon lattices.
- Numerical and theoretical models (QLS) provide consistent insights.
- Breather stability is sensitive to lattice discreteness and spacing.
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