An interface for a real-time storage oscilloscope display

Digital computer hardware and software interface for real time storage oscilloscope displa

On the boundary of the dispersion-managed soliton existence

A breathing soliton-like structure in dispersion-managed (DM) optical fiber system is studied. It is proven that for negative average dispersion the breathing soliton is forbidden provided that a modulus of average dispersion exceed a threshold which depends on the soliton amplitude.Comment: LaTeX, 8 pages, to appear in JETP Lett. 72, #3 (2000

Competing PT potentials and re-entrant PT symmetric phase for a particle in a box

We investigate the effects of competition between two complex, $\mathcal{PT}$-symmetric potentials on the $\mathcal{PT}$-symmetric phase of a "particle in a box". These potentials, given by $V_Z(x)=iZ\mathrm{sign}(x)$ and $V_\xi(x)=i\xi[\delta(x-a)-\delta(x+a)]$, represent long-range and localized gain/loss regions respectively. We obtain the $\mathcal{PT}$-symmetric phase in the $(Z,\xi)$ plane, and find that for locations $\pm a$ near the edge of the box, the $\mathcal{PT}$-symmetric phase is strengthened by additional losses to the loss region. We also predict that a broken $\mathcal{PT}$-symmetry will be restored by increasing the strength $\xi$ of the localized potential. By comparing the results for this problem and its lattice counterpart, we show that a robust $\mathcal{PT}$-symmetric phase in the continuum is consistent with the fragile phase on the lattice. Our results demonstrate that systems with multiple, $\mathcal{PT}$-symmetric potentials show unique, unexpected properties.Comment: 7 pages, 3 figure

Indicating Acts During Counting by a Chimpanzee (Pan troglodytes)

A chimpanzee (Pan troglodytes) experienced in counting arrays of 0-7 items and trained for comprehension of number symbols, spontaneously displayed a variety of indicating acts (e.g., pointing, touching, and rearranging items) during counting. Twenty-five sessions were videotaped, and all trials were evaluated for the relations among number of items presented, number of indicating acts displayed, and the Arabic number selected to represent the array. Significant correlations included the relations between number of items and the cardinal number selected by the animal, between the number of items and indicating acts displayed by the chimpanzee, and between the number of indicating acts and the numeral selected. These data suggest that the use of indicating acts by this animal may have functional significance and serves as an organizing schema, comparable to similar behaviors observed in children in the early stages of learning to count

Antisymmetric solitons and their interactions in strongly dispersion-managed fiber-optic systems

By means of the variational approximation (VA), a system of ordinary differential equations (ODEs) is derived to describe the propagation of antisymmetric solitons in a multi-channel (WDM) optical fiber link subject to strong dispersion management. Results are reported for a prototypical model including two channels. Using the VA technique, conditions for stable propagation of the antisymmetric dispersion-managed (ASDM) solitons in one channel are found, and complete and incomplete collisions between the solitons belonging to the different channels are investigated. In particular, it is shown that formation of a bound inter-channel state of two ASDM solitons is possible under certain conditions (but may be easily avoided). The VA predictions for the single- and two-channel systems are compared with direct simulations of the underlying partial differential equations. In most cases, the agreement is very good, but in some cases (very closely spaced channels) the collision may destroy the ASDM solitons. The timing-jitter suppression factor (JSF) for the ASDM soliton in one channel, and the crosstalk timing jitter induced by collision between the solitons belonging to the different channels are also estimated analytically. In particular, the JSF for the ASDM soliton may be much larger than for its fundamental-soliton counterpart in the same system.Comment: 15 pages, 10 figures, accepted for publication in Optics Communication

Families of Bragg-grating solitons in a cubic-quintic medium

We investigate the existence and stability of solitons in an optical waveguide equipped with a Bragg grating (BG) in which nonlinearity contains both cubic and quintic terms. The model has straightforward realizations in both temporal and spatial domains, the latter being most realistic. Two different families of zero-velocity solitons, which are separated by a border at which solitons do not exist, are found in an exact analytical form. One family may be regarded as a generalization of the usual BG solitons supported by the cubic nonlinearity, while the other family, dominated by the quintic nonlinearity, includes novel ``two-tier'' solitons with a sharp (but nonsingular) peak. These soliton families also differ in the parities of their real and imaginary parts. A stability region is identified within each family by means of direct numerical simulations. The addition of the quintic term to the model makes the solitons very robust: simulating evolution of a strongly deformed pulse, we find that a larger part of its energy is \emph{retained} in the process of its evolution into a soliton shape, only a small share of the energy being lost into radiation, which is opposite to what occurs in the usual BG model with cubic nonlinearity.Comment: 15 pages, 4 figures, Physics Letters A (in press

Spatial solitons in a medium composed of self-focusing and self-defocusing layers

We introduce a model combining Kerr nonlinearity with a periodically changing sign ("nonlinearity management") and a Bragg grating (BG). The main result, obtained by means of systematic simulations, is presented in the form of a soliton's stability diagram on the parameter plane of the model; the diagram turns out to be a universal one, as it practically does not depend on the soliton's power. Moreover, simulations of the nonlinear Schroedinger (NLS) model subjected to the same "nonlinearity management" demonstrate that the same diagram determines the stability of the NLS solitons, unless they are very narrow. The stability region of very narrow NLS solitons is much smaller, and soliton splitting is readily observed in that case. The universal diagram shows that a minimum non-zero average value of the Kerr coefficient is necessary for the existence of stable solitons. Interactions between identical solitons with an initial phase difference between them are simulated too in the BG model, resulting in generation of stable moving solitons. A strong spontaneous symmetry breaking is observed in the case when in-phase solitons pass through each other due to attraction between them.Comment: a latex text file and 9 eps files with figures. Physics Letters A, in pres

Instabilities of dispersion-managed solitons in the normal dispersion regime

Dispersion-managed solitons are reviewed within a Gaussian variational approximation and an integral evolution model. In the normal regime of the dispersion map (when the averaged path dispersion is negative), there are two solitons of different pulse duration and energy at a fixed propagation constant. We show that the short soliton with a larger energy is linearly (exponentially) unstable. The other (long) soliton with a smaller energy is linearly stable but hits a resonance with excitations of the dispersion map. The results are compared with the results from the recent publicationsComment: 20 figures, 20 pages. submitted to Phys. Rev.