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Floquet breathers in a modulated nonlinear lattice.
Masayuki Kimura1, Juan F R Archilla2, Yusuke Doi3
1Department of Electrical and Electronic Engineering, Faculty of Science and Engineering, Setsunan University, 17-8 Ikeda-Nakamachi, Neyagawa, Osaka 572-8508, Japan.
Chaos (Woodbury, N.Y.)
|March 31, 2026
Summary
This study explores space-time-modulated electro-mechanical systems, revealing diverse "Floquet breather" behaviors under AC current driving. These findings offer insights into dynamic metamaterials and nonlinear wave phenomena.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Metamaterials
Background:
- Space-time modulation is a key mechanism for controlling wave phenomena.
- Electromechanical systems offer tunable platforms for studying complex dynamics.
- Breathers are localized nonlinear waves crucial in various physical systems.
Purpose of the Study:
- To investigate the existence and stability of breathers in space-time-modulated electro-mechanical systems.
- To analyze the impact of AC current modulation on breather dynamics.
- To introduce the concept of "Floquet breathers" in this context.
Main Methods:
- Derivation of model equations for a coupled cantilever array.
- Extension of breather theory to incorporate space-time modulation.
- Numerical simulations to observe breather responses to modulation frequency.
Main Results:
- Identified three types of breather responses based on frequency ratios: period doubling/tripling, period-halving, and other commensurate relationships.
- Introduced and characterized "Floquet breathers" analogous to Floquet solitons.
- Observed a wide variety of breather types (site-centered, bond-centered, symmetric/antisymmetric) and analyzed their stability.
Conclusions:
- Space-time modulation provides a rich platform for generating diverse breather solutions in electro-mechanical systems.
- The concept of Floquet breathers is applicable to these systems, expanding nonlinear wave theory.
- The findings suggest potential applications in the design and study of dynamic metamaterials.
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