Discrete breathers in a nonlinear electric line: modeling, computation, and experiment

Area of Science:

• Nonlinear Dynamics
• Solid State Physics
• Electrical Engineering

Background:

• Periodic nonlinear electric lines offer a platform for studying localized nonlinear phenomena.
• Discrete breathers are localized energy modes that can exist in nonlinear discrete systems.
• Understanding breather formation and stability is crucial for potential applications in signal processing and energy localization.

Purpose of the Study:

• To experimentally and numerically investigate the existence and stability of discrete breathers in a periodic nonlinear electric line.
• To identify the parameter regimes (driver voltage and frequency) for n-peaked breather solutions.
• To examine the spontaneous formation mechanisms of these breathers.

Main Methods:

• A nonlinear electric line model comprising varactor diodes and inductors was developed.
• Numerical simulations were performed on a 32-element ring configuration.
• Experimental measurements were conducted and compared with numerical results.
• Modulational instability was analyzed to understand breather self-organization.

Main Results:

• Regions of existence and stability for n-peaked discrete breathers were identified in terms of driver voltage and frequency.
• Numerical predictions showed good quantitative agreement with experimental data.
• Spontaneous formation of n-peaked breathers via modulational instability was observed.
• Breather locations were found to be sensitive to initial conditions.

Conclusions:

• The study confirms the existence and stability of discrete breathers in nonlinear electric lines.
• The findings provide a comprehensive characterization of breather solutions and their formation dynamics.
• This research contributes to the understanding of nonlinear wave phenomena in engineered electrical systems.