Dynamics of subpicosecond dispersion-managed soliton in a fibre: A perturbative analysis

A model is studied which describes a propagation of a subpicosecond optical pulse in dispersion-managed fibre links. In the limit of weak chromatic dispersion management, the model equation is reduced to a perturbed modified NLS equation having a nonlinearity dispersion term. By means of the Riemann--Hilbert problem, a perturbation theory for the soliton of the modified NLS equation is developed. It is shown in the adiabatic approximation that there exists a unique possibility to suppress the perturbation-induced shift of the soliton centre at the cost of proper matching of the soliton width and nonlinearity dispersion parameter. In the next-order approximation, the spectral density of the radiation power emitted by a soliton is calculated.Comment: 16 pages, 3 figures, to appear in J. Mod. Optic

Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem

The hierarchy of the integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of the linearization of these equations and their conservation law in the terms of the solutions of the corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of the linearized equation due to the Noether's theorem. The local hierarchy and three nonlocal ones of the infinitesimal symmetries and the conservation laws that are explicitly expressed through the variables of the nonlinear equations are derived.Comment: 12 pages, LaTe

The Analgetic Efficacy of Pterygopalatine Blockade for Pain Treatment in Adults: a Systematic Review and Meta-Analysis

Background. The use of regional blockades for the purpose of analgesia is widely used in all fields of medicine, however, the analgesic efficacy of the pterygopalatine blockade, as an independent method of treating pain of various genesis, has not been studied enough. Therefore, there is a need to analyze the results of clinical trials to evaluate the analgesic efficacy of the pterygopalatine blockade as an independent method of anesthesia.Objective — to investigate the analgesic effect of pterygopalatine blockade as a monotherapy in patients with pain of various origins of oculotemporal area, conducting a meta-analysis of published results of randomized clinical trials.Methods. The methodology involved a systematic literature search by means of PubMed, MEDLINE, EMBASE, and Cochrane Library search engines. The search covered the period of the past 10 years and had the following criteria: a double-blind, randomized, controlled study of the use of pterygopalatine blockade with a local anesthetic versus placebo. For each included study, a standardized magnitude of the analgesic effect of pterygopalatine blockade compared to placebo was calculated, with pain assessing in 15, 30, and 60 minutes after the blockade was performed. Meta-analyses were conducted for each endpoint. Meta-analysis was performed using Stata 11.0 application programs ((The Cochrane Collaboration, Oxford, United Kingdom).Results. Five randomized controlled trials involving 269 patients met the inclusion criteria, and involved analyzing the pterygopalatine blockade with local anesthetic (n=140) against placebo (n=129). In 15 minutes after pterygopalatine blockade was performed, the difference in mean pain intensity compared to the control group was -2.5 points, the mean level was lower in the pterygopalatine blockade group, MD=-2.5 [95% CI -3.7; -1.7]. After 30 minutes: -2.7 points, MD=-2.7 [95% CI -4.5; -1.5], after 60 minutes: -1.7 points, MD=-1.7 [95% CI -4.0; -0.5]. The relative risk of adverse effects, such as nasopharyngeal symptoms, after performing a pterygopalatine blockade with a local anesthetic accounted for (RR =1.31 [95% CI 0.5–3.04]). In this regard, the incidence of complications and their variants that can be caused by pterygopalatine blockade is a matter for further clinical research.Conclusion. The results obtained in the meta-analysis testify to the analgesic effect of the pterygopalatine blockade as a monotherapy in patients with pain of different origins oculotemporal area in 15, 30, and 60 minutes after its performance. These data may be relevant when choosing a method for first-line anesthetic management of pain syndrome of oculotemporal area

INVERSE SCATTERING TRANSFORM ANALYSIS OF STOKES-ANTI-STOKES STIMULATED RAMAN SCATTERING

Zakharov-Shabat--Ablowitz-Kaup-Newel-Segur representation for Stokes-anti-Stokes stimulated Raman scattering is proposed. Periodical waves, solitons and self-similarity solutions are derived. Transient and bright threshold solitons are discussed.Comment: 16 pages, LaTeX, no figure