| 1. |
- Gorbach, A.V., et al.
(författare)
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Gap and out-gap breathers in a binary modulated discrete nonlinear Schrödinger model
- 2004
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Ingår i: European Physical Journal D. - : Springer Science and Business Media LLC. - 1434-6060 .- 1434-6079. ; 29:1, s. 77-93
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Tidskriftsartikel (refereegranskat)abstract
- We consider a modulated discrete nonlinear Schrödinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a 'forbidden' gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap - discrete gap and out-gap breathers (DGBs and DOGBs) - are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) non-linearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of 'exchange of stability' between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.
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| 2. |
- Johansson, Magnus, et al.
(författare)
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Quasiperiodic localized oscillating solutions in the discrete nonlinear Schrödinger equation with alternating on-site potential
- 2004
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Ingår i: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755. ; 70:5 2
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Tidskriftsartikel (refereegranskat)abstract
- An explicit examples of exact stable quasiperiodic localized stable solution with spatially symmetric large amplitude oscillations in a nonintegrable Hamiltonian lattice model were presented. The proposed model as observed, is a one-dimensional discrete nonlinear Schro°dinger equation with alternating on-site energies. It was observed that the pulson solutions exists for other types of multicomponent lattices with two conserved quantities. It was also observed that the pulson character of the two-frequency solution appeared when the absolute value of the minimum value of ? n0±1 exceeds the minimum value of ?n0.
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| 3. |
- Rowe, W. R., et al.
(författare)
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Gap solitons supported by mode hybridisation in Lithium Niobate nano-waveguides
- 2021
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Ingår i: 2021 Conference On Lasers And Electro-Optics Europe & European Quantum Electronics Conference (Cleo/Europe-Eqec). - : Institute of Electrical and Electronics Engineers (IEEE).
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Konferensbidrag (refereegranskat)abstract
- Nano-waveguide platforms have been developed over the past decade providing strong field enhancement and allowing precise control of modal dispersion [1] . Such nano-waveguides produced from materials with strong quadratic (χ (2) ) nonlinearity make excitation of χ (2) temporal solitons feasible [2] . Compared with Kerr solitons, χ (2) solitons have tighter dispersion criteria making nano-waveguides the only practical method for their observation [2] , [3] . As seen in previous work in photonic crystal fibres [4] , mode hybridisation, which occurs generally in waveguides with rectangular (or close to rectangular) cross-section, provides conditions to study novel types of soliton and their dynamics.
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