Soliton Interactions in Perturbed Nonlinear Schroedinger Equations

We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the nonlinear potential. We assume that the solitons are all moving with the same velocity at the initial instant; this maximizes the effect each soliton has on the others as a consequence of the perturbation. Over the long time scales that we consider, the amplitudes of the solitons remain fixed, while their center of mass coordinates obey Newton's equations with a force law for which we present an integral formula. For the interaction of two solitons with a quintic perturbation term we present more details since symmetries -- one related to the form of the perturbation and one related to the small number of particles involved -- allow the problem to be reduced to a one-dimensional one with a single parameter, an effective mass. The main results include calculations of the binding energy and oscillation frequency of nearby solitons in the stable case when the perturbation is an attractive correction to the potential and of the asymptotic "ejection" velocity in the unstable case. Numerical experiments illustrate the accuracy of the perturbative calculations and indicate their range of validity.Comment: 28 pages, 7 figures, Submitted to Phys Rev E Revised: 21 pages, 6 figures, To appear in Phys Rev E (many displayed equations moved inline to shorten manuscript

Experimental feasibility of measuring the gravitational redshift of light using dispersion in optical fibers

This paper describes a new class of experiments that use dispersion in optical fibers to convert the gravitational frequency shift of light into a measurable phase shift or time delay. Two conceptual models are explored. In the first model, long counter-propagating pulses are used in a vertical fiber optic Sagnac interferometer. The second model uses optical solitons in vertically separated fiber optic storage rings. We discuss the feasibility of using such an instrument to make a high precision measurement of the gravitational frequency shift of light.Comment: 11 pages, 12 figure

Stability of stationary states in the cubic nonlinear Schroedinger equation: applications to the Bose-Einstein condensate

The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a harmonic potential. Our comprehensive studies emphasize physical interpretations useful to experimentalists. Perturbation by stochastic white noise, phase engineering, and higher order nonlinearity are considered. We treat both attractive and repulsive nonlinearity and illustrate the soliton-train nature of the stationary states.Comment: 9 pages, 11 figure

Potential of novel Mycobacterium tuberculosis infection phase-dependent antigens in the diagnosis of TB disease in a high burden setting

<p>Abstract</p> <p>Background</p> <p>Confirming tuberculosis (TB) disease in suspects in resource limited settings is challenging and calls for the development of more suitable diagnostic tools. Different <it>Mycobacterium tuberculosis (M.tb) </it>infection phase-dependent antigens may be differentially recognized in infected and diseased individuals and therefore useful as diagnostic tools for differentiating between <it>M.tb </it>infection states. In this study, we assessed the diagnostic potential of 118 different <it>M.tb </it>infection phase-dependent antigens in TB patients and household contacts (HHCs) in a high-burden setting.</p> <p>Methods</p> <p>Antigens were evaluated using the 7-day whole blood culture technique in 23 pulmonary TB patients and in 19 to 21 HHCs (total n = 101), who were recruited from a high-TB incidence community in Cape Town, South Africa. Interferon-gamma (IFN-γ) levels in culture supernatants were determined by ELISA.</p> <p>Results</p> <p>Eight classical TB vaccine candidate antigens, 51 DosR regulon encoded antigens, 23 TB reactivation antigens, 5 TB resuscitation promoting factors (rpfs), 6 starvation and 24 other stress response-associated TB antigens were evaluated in the study. The most promising antigens for ascertaining active TB were the rpfs (Rv0867c, Rv2389c, Rv2450c, Rv1009 and Rv1884c), with Areas under the receiver operating characteristics curves (AUCs) between 0.72 and 0.80. A combination of <it>M.tb </it>specific ESAT-6/CFP-10 fusion protein, Rv2624c and Rv0867c accurately predicted 73% of the TB patients and 80% of the non-TB cases after cross validation.</p> <p>Conclusions</p> <p>IFN-γ responses to TB rpfs show promise as TB diagnostic candidates and should be evaluated further for discrimination between <it>M.tb </it>infection states.</p

EMA401, an orally administered highly selective angiotensin II type 2 receptor antagonist, as a novel treatment for postherpetic neuralgia: a randomised, double-blind, placebo-controlled phase 2 clinical trial.

BACKGROUND: Existing treatments for postherpetic neuralgia, and for neuropathic pain in general, are limited by modest efficacy and unfavourable side-effects. The angiotensin II type 2 receptor (AT2R) is a new target for neuropathic pain. EMA401, a highly selective AT2R antagonist, is under development as a novel neuropathic pain therapeutic agent. We assessed the therapeutic potential of EMA401 in patients with postherpetic neuralgia. METHODS: In this multicentre, placebo-controlled, double-blind, randomised, phase 2 clinical trial, we enrolled patients (aged 22-89 years) with postherpetic neuralgia of at least 6 months' duration from 29 centres across six countries. We randomly allocated 183 participants to receive either oral EMA401 (100 mg twice daily) or placebo for 28 days. Randomisation was done according to a centralised randomisation schedule, blocked by study site, which was generated by an independent, unmasked statistician. Patients and staff at each site were masked to treatment assignment. We assessed the efficacy, safety, and pharmacokinetics of EMA401. The primary efficacy endpoint was change in mean pain intensity between baseline and the last week of dosing (days 22-28), measured on an 11-point numerical rating scale. The primary efficacy analysis was intention to treat. This trial is registered with the Australian New Zealand Clinical Trials Registry, number ACTRN12611000822987. FINDINGS: 92 patients were assigned to EMA401 and 91 were assigned to placebo. The patients given EMA401 reported significantly less pain compared with baseline values in the final week of treatment than did those given placebo (mean reductions in pain scores -2.29 [SD 1.75] vs -1.60 [1.66]; difference of adjusted least square means -0.69 [SE 0.25]; 95% CI -1.19 to -0.20; p=0.0066). No serious adverse events related to EMA401 occurred. Overall, 32 patients reported 56 treatment-emergent adverse events in the EMA401 group compared with 45 such events reported by 29 patients given placebo. INTERPRETATION: EMA401 (100 mg twice daily) provides superior relief of postherpetic neuralgia compared with placebo at the end of 28 days of treatment. EMA401 was well tolerated by patients. FUNDING: Spinifex Pharmaceuticals