Soliton formation from a pulse passing the zero-dispersion point in a nonlinear Schr\"odinger equation

We consider in detail the self-trapping of a soliton from a wave pulse that passes from a defocussing region into a focussing one in a spatially inhomogeneous nonlinear waveguide, described by a nonlinear Schrodinger equation in which the dispersion coefficient changes its sign from normal to anomalous. The model has direct applications to dispersion-decreasing nonlinear optical fibers, and to natural waveguides for internal waves in the ocean. It is found that, depending on the (conserved) energy and (nonconserved) mass of the initial pulse, four qualitatively different outcomes of the pulse transformation are possible: decay into radiation; self-trapping into a single soliton; formation of a breather; and formation of a pair of counterpropagating solitons. A corresponding chart is drawn on a parametric plane, which demonstrates some unexpected features. In particular, it is found that any kind of soliton(s) (including the breather and counterpropagating pair) eventually decays into pure radiation with the increase of the energy, the initial mass being kept constant. It is also noteworthy that a virtually direct transition from a single soliton into a pair of symmetric counterpropagating ones seems possible. An explanation for these features is proposed. In two cases when analytical approximations apply, viz., a simple perturbation theory for broad initial pulses, or the variational approximation for narrow ones, comparison with the direct simulations shows reasonable agreement.Comment: 18 pages, 10 figures, 1 table. Phys. Rev. E, in pres

The Modulation of Multiple Phases Leading to the Modified KdV Equation

This paper seeks to derive the modified KdV (mKdV) equation using a novel approach from systems generated from abstract Lagrangians that possess a two-parameter symmetry group. The method to do uses a modified modulation approach, which results in the mKdV emerging with coefficients related to the conservation laws possessed by the original Lagrangian system. Alongside this, an adaptation of the method of Kuramoto is developed, providing a simpler mechanism to determine the coefficients of the nonlinear term. The theory is illustrated using two examples of physical interest, one in stratified hydrodynamics and another using a coupled Nonlinear Schr\"odinger model, to illustrate how the criterion for the mKdV equation to emerge may be assessed and its coefficients generated.Comment: 35 pages, 5 figure

Cuspons, peakons and regular gap solitons between three dispersion curves

A general wave model with the cubic nonlinearity is introduced to describe a situation when the linear dispersion relation has three branches, which would intersect in the absence of linear couplings between the three waves. Actually, the system contains two waves with a strong linear coupling between them, to which a third wave is then coupled. This model has two gaps in its linear spectrum. Realizations of this model can be made in terms of temporal or spatial evolution of optical fields in, respectively, a planar waveguide or a bulk-layered medium resembling a photonic-crystal fiber. Another physical system described by the same model is a set of three internal wave modes in a density-stratified fluid. A nonlinear analysis is performed for solitons which have zero velocity in the reference frame in which the group velocity of the third wave vanishes. Disregarding the self-phase modulation (SPM) term in the equation for the third wave, we find two coexisting families of solitons: regular ones, which may be regarded as a smooth deformation of the usual gap solitons in a two-wave system, and cuspons with a singularity in the first derivative at their center. Even in the limit when the linear coupling of the third wave to the first two vanishes, the soliton family remains drastically different from that in the linearly uncoupled system; in this limit, regular solitons whose amplitude exceeds a certain critical value are replaced by peakons. While the regular solitons, cuspons, and peakons are found in an exact analytical form, their stability is tested numerically, which shows that they all may be stable. If the SPM terms are retained, we find that there again coexist two different families of generic stable soliton solutions, namely, regular ones and peakons.Comment: a latex file with the text and 10 pdf files with figures. Physical Review E, in pres

Stable embedded solitons

Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numerical simulations. These results establish that, contrary to previous beliefs, embedded solitons can be robust despite being in resonance with the linear spectrum.Comment: 2 figures. To appear in Phys. Rev. Let

Unsteady undular bores in fully nonlinear shallow-water theory

We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully nonlinear dispersive terms. This system contains one horizontal space dimension and time and can be systematically derived from the full Euler equations for irrotational flows with a free surface using a standard long-wave asymptotic expansion. In this context the system was first derived by Su and Gardner. It coincides with the one-dimensional flat-bottom reduction of the Green-Naghdi system and, additionally, has recently found a number of fluid dynamics applications other than the present context of shallow-water gravity waves. We then use the Whitham modulation theory for a one-phase periodic travelling wave to obtain an asymptotic analytical description of an undular bore in the Su-Gardner system for a full range of "depth" ratios across the bore. The positions of the leading and trailing edges of the undular bore and the amplitude of the leading solitary wave of the bore are found as functions of this "depth ratio". The formation of a partial undular bore with a rapidly-varying finite-amplitude trailing wave front is predicted for ``depth ratios'' across the bore exceeding 1.43. The analytical results from the modulation theory are shown to be in excellent agreement with full numerical solutions for the development of an undular bore in the Su-Gardner system.Comment: Revised version accepted for publication in Phys. Fluids, 51 pages, 9 figure

Implementation of a national HIV pre-exposure prophylaxis service is associated with changes in characteristics of people with newly diagnosed HIV: a retrospective cohort study

OBJECTIVES: To review characteristics of individuals newly diagnosed with HIV following implementation of a national pre-exposure prophylaxis (PrEP) programme (comprehensive PrEP services, delivered in sexual health clinics) to inform future delivery and broader HIV prevention strategies. METHODS: We extracted data from national HIV databases (July 2015-June 2018). We compared sociodemographic characteristics of individuals diagnosed in the period before and after PrEP implementation, and determined the proportion of 'potentially preventable' infections with the sexual health clinic-based PrEP delivery model used. RESULTS: Those diagnosed with HIV before PrEP implementation were more likely to be male (342/418, 81.8% vs 142/197, 72.1%, p=0.005), be white indigenous (327/418, 78.2% vs 126/197, 64.0%, p<0.001), report transmission route as sex between men (219/418, 52.4% vs 81/197, 41.1%, p=0.014), and have acquired HIV in the country of the programme (302/418, 72.2% vs 114/197, 57.9% p<0.001) and less likely to report transmission through heterosexual sex (114/418, 27.3% vs 77/197, 39.1%, p=0.002) than after implementation.Pre-implementation, 8.6% (36/418) diagnoses were 'potentially preventable' with the PrEP model used. Post-implementation, this was 6.6% (13/197), but higher among those with recently acquired HIV (49/170, 28.8%). Overall, individuals with 'potentially preventable' infections were more likely to be male (49/49, 100% vs 435/566, 76.9%, p<0.001), aged <40 years (37/49, 75.5% vs 307/566, 54.2%, p=0.004), report transmission route as sex between men (49/49, 100% vs 251/566, 44.3%, p<0.001), have previously received post-exposure prophylaxis (12/49, 24.5% vs 7/566, 1.2%, p<0.001) and less likely to be black African (0/49, 0% vs 67/566, 11.8%, p=0.010) than those not meeting this definition. CONCLUSIONS: The sexual health clinic-based national PrEP delivery model appeared to best suit men who have sex with men and white indigenous individuals but had limited reach into other key vulnerable groups. Enhanced models of delivery and HIV combination prevention are required to widen access to individuals not benefiting from PrEP at present

Developing the content of two behavioural interventions : using theory-based interventions to promote GP management of upper respiratory tract infection without prescribing antibiotics #1

Background: Evidence shows that antibiotics have limited effectiveness in the management of upper respiratory tract infection (URTI) yet GPs continue to prescribe antibiotics. Implementation research does not currently provide a strong evidence base to guide the choice of interventions to promote the uptake of such evidence-based practice by health professionals. While systematic reviews demonstrate that interventions to change clinical practice can be effective, heterogeneity between studies hinders generalisation to routine practice. Psychological models of behaviour change that have been used successfully to predict variation in behaviour in the general population can also predict the clinical behaviour of healthcare professionals. The purpose of this study was to design two theoretically-based interventions to promote the management of upper respiratory tract infection (URTI) without prescribing antibiotics. Method: Interventions were developed using a systematic, empirically informed approach in which we: selected theoretical frameworks; identified modifiable behavioural antecedents that predicted GPs intended and actual management of URTI; mapped these target antecedents on to evidence-based behaviour change techniques; and operationalised intervention components in a format suitable for delivery by postal questionnaire. Results: We identified two psychological constructs that predicted GP management of URTI: "Self-efficacy," representing belief in one's capabilities, and "Anticipated consequences," representing beliefs about the consequences of one's actions. Behavioural techniques known to be effective in changing these beliefs were used in the design of two paper-based, interactive interventions. Intervention 1 targeted self-efficacy and required GPs to consider progressively more difficult situations in a "graded task" and to develop an "action plan" of what to do when next presented with one of these situations. Intervention 2 targeted anticipated consequences and required GPs to respond to a "persuasive communication" containing a series of pictures representing the consequences of managing URTI with and without antibiotics. Conclusion: It is feasible to systematically develop theoretically-based interventions to change professional practice. Two interventions were designed that differentially target generalisable constructs predictive of GP management of URTI. Our detailed and scientific rationale for the choice and design of our interventions will provide a basis for understanding any effects identified in their evaluation. Trial registration: Clinicaltrials.gov NCT00376142This study is funded by the European Commission Research Directorate as part of a multi-partner program: Research Based Education and Quality Improvement (ReBEQI): A Framework and tools to develop effective quality improvement programs in European healthcare. (Proposal No: QLRT-2001-00657)

Evaluation of the fidelity of an interactive face-to-face educational intervention to improve general practitioner management of back pain

OBJECTIVES: Implementation intervention effects can only be fully realised and understood if they are faithfully delivered. However the evaluation of implementation intervention fidelity is not commonly undertaken. The IMPLEMENT intervention was designed to improve the management of low back pain by general medical practitioners. It consisted of a two-session interactive workshop, including didactic presentations and small group discussions by trained facilitators. This study aimed to evaluate the fidelity of the IMPLEMENT intervention by assessing: (1) observed facilitator adherence to planned behaviour change techniques (BCTs); (2) comparison of observed and self-reported adherence to planned BCTs and (3) variation across different facilitators and different BCTs. DESIGN: The study compared planned and actual, and observed versus self-assessed delivery of BCTs during the IMPLEMENT workshops. METHOD: Workshop sessions were audiorecorded and transcribed verbatim. Observed adherence of facilitators to the planned intervention was assessed by analysing the workshop transcripts in terms of BCTs delivered. Self-reported adherence was measured using a checklist completed at the end of each workshop session and was compared with the 'gold standard' of observed adherence using sensitivity and specificity analyses. RESULTS: The overall observed adherence to planned BCTs was 79%, representing moderate-to-high intervention fidelity. There was no significant difference in adherence to BCTs between the facilitators. Sensitivity of self-reported adherence was 95% (95% CI 88 to 98) and specificity was 30% (95% CI 11 to 60). CONCLUSIONS: The findings suggest that the IMPLEMENT intervention was delivered with high levels of adherence to the planned intervention protocol. TRIAL REGISTRATION NUMBER: The IMPLEMENT trial was registered in the Australian New Zealand Clinical Trials Registry, ACTRN012606000098538 (http://www.anzctr.org.au/trial_view.aspx?ID=1162)

Self-management interventions to improve skin care for pressure ulcer prevention in people with spinal cord injuries: A systematic review protocol

Background: Pressure ulcers are a serious, common, lifelong, and costly secondary complication of spinal cord injury (SCI). Community-dwelling people with a SCI can prevent them with appropriate skin care (i.e. pressure relieving activities, skin checks). Adherence to skin care remains suboptimal however, and self-management interventions that focus on improving this have been designed. Little is known on their content, effectiveness, or theoretical basis. The aim of the proposed systematic review is to synthesize the literature on self-management interventions to improve skin care in people with a SCI. Specific objectives are to describe these interventions in relation to their content, effectiveness, theory base, and adherence to reporting guidelines for intervention description. Methods: The search strategy will combine an electronic search of nine bibliographic databases (MEDLINE, Embase, PsycInfo, CENTRAL, CINAHL, Rehabdata, CIRRIE, PEDro, ERIC) and two trial registers with a manual search of relevant reference lists. Predefined eligibility criteria will be applied in a two-phase selection process involving title and abstract screening, followed by full-text screening. A data extraction spreadsheet will be applied to included papers. Intervention content will be coded using two taxonomies (behaviour change taxonomy; PRISMS self-management support taxonomy). A validated tool (Theory Coding Scheme) and the Template for Intervention Description and Replication (TIDieR) will be used to examine theoretical basis and assess adherence to reporting guidelines for intervention description. A small number of heterogeneous studies are likely to be included in this review therefore a narrative synthesis is planned. Discussion: This systematic review will help identify the gaps and priorities to guide future research activities in this area. Systematic review registration: PROSPERO CRD4201603319