Quasiperiodic and chaotic discrete breathers in a parametrically driven system without linear dispersion.

Area of Science:

• Nonlinear dynamics
• Condensed matter physics
• Lattice dynamics

Background:

• Discrete breathers (DBs) are localized nonlinear excitations in discrete systems.
• Anharmonic lattices exhibit complex dynamics under external forcing.
• Understanding breather stability is crucial for energy localization applications.

Purpose of the Study:

• To investigate the construction and stability of discrete breathers in a 1D lattice with quartic interactions.
• To explore the effect of parametric periodic driving on breather localization and stability.
• To analyze the transition from stable quasiperiodic breathers to chaotic states.

Main Methods:

• Exact construction of discrete breathers by separating time and space dependence.
• Utilizing homoclinic orbits and Poincaré sections of a Duffing equation for spatial profiles and initial conditions.
• Employing parametric periodic driving and varying driving amplitude for stabilization.
• Analyzing breather behavior near resonance islands and chaotic layers.

Main Results:

• Explicit construction of discrete breathers (DBs) with specific spatial profiles.
• Stabilization of DBs through parametric driving, leading to long-lived quasiperiodic breathers.
• Observation of breather destabilization and transition to chaotic states near chaotic layers.
• Identification of large stable regions (tori) in phase space around DB solutions, attributed to the absence of phonon resonances.

Conclusions:

• Parametric driving offers a robust method for stabilizing discrete breathers in anharmonic lattices.
• The absence of phonon resonances facilitates strong localization phenomena.
• Stable quasiperiodic breathers can exist even in the presence of weak linear dispersion, suggesting broader applicability.