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We prove the existence of a class of time-localized and space-periodic breathers (called q-gap breathers) in nonlinear lattices with time-periodic coe!cients. These q-gap breathers are the counterparts to the classical space-localized and time-periodic breathers found in space-periodic systems. Using normal form transformations, we establish rigorously the existence of such solutions with oscillating tails (in the time domain) that can be made arbitrarily small but finite. Due to the presence of the oscillating tails, these solutions are coined generalized q-gap breathers. Using a multiple-scale analysis, we also derive a tractable amplitude equation that describes the dynamics of breathers in the limit of small amplitude. In the presence of damping, we demonstrate the existence of transition fronts that connect the trivial state to the time-periodic ones. The analytical results are corroborated by systematic numerical simulations.
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Modulation instability and wavenumber bandgap breathers in a time layered phononic lattice
We provide the first experimental realization of wavenumber bandgap (𝑞−gap) breathers. Experiments are obtained in the setting of a time-periodic phononic lattice where the model and experiment exhibit good qualitative agreement. 𝑞−gap breathers are localized in time and periodic in space, and are the counterparts to the classical breathers found in space-periodic systems. We derive an exact condition for modulation instability that leads to the opening of wavenumber bandgaps in which the 𝑞−gap breathers can arise. The 𝑞−gap breathers become more narrow and larger in amplitude as the wavenumber goes further into the bandgap. In the presence of damping, these structures acquire a nonzero, oscillating tail. The controllable temporal localization that 𝑞−gap breathers make possible has potential applications in the creation of phononic frequency combs, energy harvesting or acoustic signal processing.
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- PAR ID:
- 10511903
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Research
- Volume:
- 6
- Issue:
- 2
- ISSN:
- 2643-1564
- Subject(s) / Keyword(s):
- Breathers nonlinear lattice wavenumber bandgap
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevResearch.6.023045
