Browsing by Author "Frantzeskakis, D. J."

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    Dark soliton scattering in symmetric and asymmetric double potential barriers
    (Elsevier, 2017-06-01) Tsitoura, F.; Anastassi, Zacharias; Marzuola, J. L.; Kevrekidis, P. G.; Frantzeskakis, D. J.
    Motivated by the recent theoretical study of (bright) soliton diode effects in systems with multiple scatterers, as well as by experimental investigations of soliton-impurity interactions, we consider some prototypical case examples of interactions of dark solitons with a pair of scatterers. In a way fundamentally opposite to the case of bright solitons (but consonant to their “anti-particle character”), we find that dark solitons accelerate as they pass the first barrier and hence cannot be trapped by a second equal-height barrier. A pair of unequal barriers may lead to reflection from the second one, however trapping in the inter-barrier region cannot occur. We also give some examples of dynamical adjusting of the barriers to trap the dark soliton in the inter-barrier region, yet we show that this can only occur over finite time horizons, with the dark soliton always escaping eventually, contrary again to what is potentially the case with bright solitons.
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    Dark solitons near potential and nonlinearity steps
    (American Physical Society, 2016-12-14) Tsitoura, F.; Anastassi, Zacharias; Marzuola, J. L.; Kevrekidis, P. G.; Frantzeskakis, D. J.
    We study dark solitons near potential and nonlinearity steps and combinations thereof, forming rectangular barriers. This setting is relevant to the contexts of atomic Bose-Einstein condensates (where such steps can be realized by using proper external fields) and nonlinear optics (for beam propagation near interfaces separating optical media of different refractive indices).We use perturbation theory to develop an equivalent particle theory, describing the matter-wave or optical soliton dynamics as the motion of a particle in an effective potential. This Newtonian dynamical problem provides information for the soliton statics and dynamics, including scenarios of reflection, transmission, or quasitrapping at such steps. The case of multiple such steps and its connection to barrier potentials is additionally touched upon. The range of validity of the analytical approximation and radiation effects are also investigated. Our analytical predictions are found to be in very good agreement with the corresponding numerical results, where appropriate.
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    Spatiotemporal algebraically localized waveforms for a nonlinear Schrödinger model with gain and loss
    (Elsevier, 2017-06-27) Anastassi, Zacharias; Fotopoulos, G.; Frantzeskakis, D. J.; Horikis, T. P.; Karachalios, N. I.; Kevrekidis, P. G.; Stratis, I. G.; Vetas, K.
    We consider the asymptotic behavior of the solutions of a nonlinear Schrödinger (NLS) model incorporating linear and nonlinear gain/loss. First, we describe analytically the dynamical regimes (depending on the gain/loss strengths), for finite-time collapse, decay, and global existence of solutions. Then, for all the above parametric regimes, we use direct numerical simulations to study the dynamics corresponding to algebraically decaying initial data. We identify crucial differences between the dynamics of vanishing initial conditions, and those converging to a finite constant background: in the former (latter) case we find strong (weak) collapse or decay, when the gain/loss parameters are selected from the relevant regimes. One of our main results, is that in all the above regimes, non-vanishing initial data transition through spatiotemporal, algebraically decaying waveforms. While the system is nonintegrable, the evolution of these waveforms is reminiscent to the evolution of the Peregrine rogue wave of the integrable NLS limit. The parametric range of gain and loss for which this phenomenology persists is also touched upon.