Journal ArticleDOI
Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
Robert S. MacKay,Serge Aubry +1 more
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In this paper, the existence of time-periodic, spatially localized solutions for weakly coupled oscillators is proved for a broad range of time reversible or Hamiltonian networks.Abstract:
Existence of 'breathers', that is, time-periodic, spatially localized solutions, is proved for a broad range of time-reversible or Hamiltonian networks of weakly coupled oscillators. Some of their properties are discussed, some generalizations suggested, and several open questions raised.read more
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Fano resonances in nanoscale structures
TL;DR: In this paper, the authors introduce the concept of Fano resonances, which can be reduced to the interaction of a discrete (localized) state with a continuum of propagation modes, and explain their geometrical and/or dynamical origin.
Journal ArticleDOI
Nonlinear waves in PT -symmetric systems
TL;DR: The concept of parity-time symmetric systems is rooted in non-Hermitian quantum mechanics where complex potentials obeying this symmetry could exhibit real spectra as discussed by the authors, which has applications in many fields of physics, e.g., in optics, metamaterials, acoustics, Bose-Einstein condensation, electronic circuitry, etc.
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Discrete Breathers
Sergej Flach,C. R. Willis +1 more
TL;DR: In this article, the existence of discrete breathers in nonlinear classical Hamiltonian lattices has been studied and existence proofs, necessary existence conditions, and structural stability of such breathers have been discussed, as well as potential applications in lattice dynamics of solids.
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Discrete breathers — Advances in theory and applications
Sergej Flach,Andrey V. Gorbach +1 more
TL;DR: In this paper, the authors introduce the concept of localized excitations and review their basic properties including dynamical and structural stability, and focus on advances in the theory of discrete breathers in three directions.
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Breathers in nonlinear lattices: existence, linear stability and quantization
TL;DR: In this article, it was shown that there exist spatially localized and time periodic solutions (breathers) in arrays of nonlinear coupled classical oscillators provided the coupling is not too strong.
References
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Journal ArticleDOI
The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
Journal ArticleDOI
Entropy-driven DNA denaturation.
TL;DR: Transfer-integral calculations show that this one-dimensional model, without including long-range interactions, exhibits a sharp denaturation reminiscent of a first-order transition at a temperature lower than a similar model with harmonic coupling.
Book
Nearly Integrable Infinite-Dimensional Hamiltonian Systems
TL;DR: Symplectic structures and hamiltonian systems in scales of hilbert spaces were shown to exist in this article, and the main theorem was proved in terms of the following properties: