Integrable discretizations of the sine-Gordon equation

The inverse scattering theory for the sine-Gordon equation discretized in space and both in space and time is considered.Comment: 18 pages, LaTeX2

Gap soliton formation by nonlinear supratransmission in Bragg media

A Bragg medium in the nonlinear Kerr regime, submitted to incident cw-radiation at a frequency in a band gap, switches from total reflection to transmission when the incident energy overcomes some threshold. We demonstrate that this is a result of nonlinear supratransmission, which allows to prove that i) the threshold incident amplitude is simply expressed in terms of the deviation from the Bragg resonance, ii) the process is not the result of a shift of the gap in the nonlinear dispersion relation, iii) the transmission does occur by means of gap soliton trains, as experimentally observed [D. Taverner et al., Opt Lett 23 (1998) 328], iv) the required energy tends to zero close to the band edge.Comment: 5 figures, submitted to EuroPhysics Letter

On dissipationless shock waves in a discrete nonlinear Schr\"odinger equation

It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless limit these equations lead to wave breaking phenomenon for general enough initial conditions, and, after taking into account small dispersion effects, result in formation of dissipationless shock waves. The Whitham theory of modulations of nonlinear waves is used for analytical description of such waves.Comment: 15 pages, 9 figure

Factors associated with antiretroviral treatment initiation amongst HIV-positive individuals linked to care within a universal test and treat programme: early findings of the ANRS 12249 TasP trial in rural South Africa

Prompt uptake of antiretroviral treatment (ART) is essential to ensure the success of universal test and treat (UTT) strategies to prevent HIV transmission in high-prevalence settings. We describe ART initiation rates and associated factors within an ongoing UTT cluster-randomized trial in rural South Africa. HIV-positive individuals were offered immediate ART in the intervention arm vs. national guidelines recommended initiation (CD4≤350 cells/mm3) in the control arm. We used data collected up to July 2015 among the ART-eligible individuals linked to TasP clinics before January 2015. ART initiation rates at one (M1), three (M3) and six months (M6) from baseline visit were described by cluster and CD4 count strata (cells/mm3) and other eligibility criteria: ≤100; 100–200; 200–350; CD4>350 with WHO stage 3/4 or pregnancy; CD4>350 without WHO stage 3/4 or pregnancy. A Cox model accounting for covariate effect changes over time was used to assess factors associated with ART initiation. The 514 participants had a median [interquartile range] follow-up duration of 1.08 [0.69; 2.07] months until ART initiation or last visit. ART initiation rates at M1 varied substantially (36.9% in the group CD4>350 without WHO stage 3/4 or pregnancy, and 55.2–71.8% in the three groups with CD4≤350) but less at M6 (from 85.3% in the first group to 96.1–98.3% in the three other groups). Factors associated with lower ART initiation at M1 were a higher CD4 count and attending clinics with both high patient load and higher cluster HIV prevalence. After M1, having a regular partner was the only factor associated with higher likelihood of ART initiation. These findings suggest good ART uptake within a UTT setting, even among individuals with high CD4 count. However, inadequate staffing and healthcare professional practices could result in prioritizing ART initiation in patients with the lowest CD4 counts

An integrable discretization of KdV at large times

An "exact discretization" of the Schroedinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can be solved by using this spectral transform and that for a special choice of the constants it can be considered an integrable discretization of the KdV equation at large times. An integrable difference-difference equation is also obtained.Comment: 12 page

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consistent way as soon as the spectral transform vanishes with 1/k at infinity in the whole upper half plane (where it may possess single poles) and is continuous and bounded on the real k-axis. The method is applied to stimulated Raman scattering and sine-Gordon (light cone) for which it is demonstrated that time evolution conserves the properties of the spectral transform.Comment: LaTex file, 1 figure, submitted to J. Phys.

Influence of melengesterol acetate (MGA®) and Implus-H® implants on rate of gain, feed efficiency, and carcass characteristics of culled beef cows fed a high concentrate ration

No statistical differences were detected in feedlot performance or carcass traits between control culled beef cows and those that were treated with melengesterol acetate (MGA®) and/or Implus-H® when fed in a feedyard for 56 days before slaughter. All groups performed well, indicating that this practice may be used to improve the market value of culled cows. Cow health during the feeding period is a major concern

Nonlinear energy transmission in the gap

Numerical simulations of the scattering of a linear plane wave incoming onto a nonlinear medium (sine-Gordon) reveals that: i) nonlinearity allows energy transmission in the forbidden band, ii) this nonlinear transmission occurs beyond an energy threshold of the incoming wave, iii) the process begins (at the threshold) with large amplitude breathers, and then energy is generically transmitted both by kink-antikink pairs and breathers.Comment: Latex file, 6 figures, 9 pages, to appear in Physics Letters