Wave envelopes with second-order spatiotemporal dispersion : I. Bright Kerr solitons and cnoidal waves

We propose a simple scalar model for describing pulse phenomena beyond the conventional slowly-varying envelope approximation. The generic governing equation has a cubic nonlinearity and we focus here mainly on contexts involving anomalous group-velocity dispersion. Pulse propagation turns out to be a problem firmly rooted in frames-of-reference considerations. The transformation properties of the new model and its space-time structure are explored in detail. Two distinct representations of exact analytical solitons and their associated conservation laws (in both integral and algebraic forms) are presented, and a range of new predictions is made. We also report cnoidal waves of the governing nonlinear equation. Crucially, conventional pulse theory is shown to emerge as a limit of the more general formulation. Extensive simulations examine the role of the new solitons as robust attractors

Wave envelopes with second-order spatiotemporal dispersion: II. Modulational instabilities and dark Kerr solitons

A simple scalar model for describing spatiotemporal dispersion of pulses, beyond the classic “slowly-varying envelopes + Galilean boost” approach, is studied. The governing equation has a cubic nonlinearity and we focus here mainly on contexts with normal group-velocity dispersion. A complete analysis of continuous waves is reported, including their dispersion relations and modulational instability characteristics. We also present a detailed derivation of exact analytical dark solitons, obtained by combining direct-integration methods with geometrical transformations. Classic results from conventional pulse theory are recovered as-ymptotically from the spatiotemporal formulation. Numerical simulations test new theoretical predictions for modulational instability, and examine the robustness of spatiotemporal dark solitons against perturbations to their local pulse shape

Flat bidifferential ideals and semihamiltonian PDEs

In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law. The density and the current of this conservation law satisfy a second order system of PDEs which has a natural interpretation in the theory of flat bifferential ideals. The class of systems we consider contains important well-known examples of semihamiltonian systems. Other examples, like genus 1 Whitham modulation equations for KdV, are related to this class by a reciprocal trasformation.Comment: 18 pages. v5: formula (36) corrected; minor change

Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media

We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in appearance of stability (instability) bands in focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolor periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns.Comment: 29 pages, 10 figure

Singular sectors of the 1-layer Benney and dToda systems and their interrelations

Complete description of the singular sectors of the 1-layer Benney system (classical long wave equation) and dToda system is presented. Associated Euler-Poisson-Darboux equations E(1/2,1/2) and E(-1/2,-1/2) are the main tool in the analysis. A complete list of solutions of the 1-layer Benney system depending on two parameters and belonging to the singular sector is given. Relation between Euler-Poisson-Darboux equations E(a,a) with opposite sign of a is discussed.Comment: 15 pages; Theor. Mathem. Physics, 201

Postoperative prolonged infiltration anesthesia for multimodal perioperative pain management in patients with hip replacement arthroplasty

ТАЗОБЕДРЕННЫЙ СУСТАВ /ХИРТОТАЛЬНОЕ ЭНДОПРОТЕЗИРОВАНИЕАНЕСТЕЗИЯ ЭПИДУРАЛЬНАЯАНЕСТЕЗИЯ МЕСТНАЯАНЕСТЕЗИЯ ИНФИЛЬТРАЦИОННАЯРОПИВАКАИНА ГИДРОХЛОРИДМИКРОИНФУЗИОННАЯ ПОМПАЦель. Улучшить эффективность мультимодального периоперационного обезболивания у пациентов при тотальном эндопротезировании тазобедренного сустава за счет применения послеоперационной пролонгированной инфильтрационной анестезии области оперативного вмешательства. Материал и методы. Проведен проспективный сравнительный анализ результатов лечения 78 пациентов, которым было выполнено первичное тотальное эндопротезирование тазобедренного сустава. Пациенты были разделены на две группы: в первой группе в послеоперационном периоде использовали продленную эпидуральную анальгезию, во второй группе применяли пролонгированную 24-часовую инфильтрационную анестезию области операции введением 0,2% раствора ропивакаина гидрохлорида с помощью микроинфузионной помпы с постоянной скоростью 8 мл/час. У всех пациентов анализировали выраженность болевого синдрома, уровень плазменной концентрации кортизола, уровень гликемии. Также оценивали расход тримеперидина и время начала активизации пациентов. Оценку проводили за 24 часа до операции, а также через 6 и 24 часа после нее. Результаты. Через 24 часа после операции в первой и второй группах выраженность боли по шкале ВАШ составила 2,2±0,35 и 1,5±0,42 балла соответственно; уровень плазменного кортизола составил 768,5±45,8 нмоль/л и 584,6±54,2 нмоль/л соответственно; уровень концентрации глюкозы в крови составил 7,03±0,34 ммоль/л и 5,91±0,27 ммоль/л соответственно. Количество использованного тримеперидина за первые 24 часа после операции в первой и второй группах составило 38,6±2,95 мг и 21,3±3,17 мг соответственно. Первое присаживание и вертикализацию пациентов в первой группе осуществляли через 24,8±2,4 и 28±1,4 часа, во второй клинической группе – через 4,5±0,5 и 6,3±0,7 часа соответственно. Заключение. Применение пролонгированной инфильтрационной анестезии позволило на 46,7% эффективнее купировать болевой синдром, на 55,2% снизить количество требуемого тримеперидина в течение первых суток после операции и на 20,3±1,4 часа раньше начать активизацию пациентов по сравнению с продленной эпидуральной анестезией.Objective. To improve the efficiency of multimodal perioperative pain management in patients in case of the hip replacement arthroplasty using postoperative prolonged infiltration anesthesia in the area of surgical intervention. Methods. A prospective comparative analysis of the treatment results of 78 patients underwent the primary hip replacement arthroplasty was performed. The patients were divided into two groups: (1) the first group of patients was treated with prolonged epidural analgesia in the postoperative period, while (2) in the second group, the patients were treated with prolonged 24-hour infiltration anesthesia at the area of the surgical intervention by 0.2% of the ropivacaine hydrochloride solution, administered using microinfusion pump with a constant rate of 8 ml per hour. All patients were assessed for intensity of the pain syndrome, plasma concentrations of the cortisol and blood glucose levels. Also, trimeperidine consumption rate and the start of patient’s activity were assessed. The evaluation was conducted 24 hours prior to the surgical intervention, as well as 6 and 24 hours after. Results. 24 hours after the surgery, the pain intensity scores assessed by the VAS were 2.2±0.35 and 1.5±0.42 points in the first and second clinical groups, respectively; the cortisol plasma levels 24 hours after the surgical intervention were 768.5±45.8 nmol/l and 584.6±54.2 nmol/l in the first and second clinical groups, respectively; the blood glucose levels after the surgical intervention were 7.03±0.34 mmol/l and 5.91±0.27 mmol/l in the first and second clinical groups, respectively. Trimeperidine consumption rates for the first 24 hours after the surgical intervention were 38.6±2.95 mg and 21.3±3.17 mg in the first and second clinical groups, respectively. The first sitting and complete verticalization of patients in the first group were performed in 24.8±2.4 and 28±1.4 hours, while in the second clinical group, these activities were performed in 4.5±0.5 and 6.3±0.7 hours respectively. Conclusions. The use of the prolonged infiltration anesthesia allowed by 46.7% more effectively arresting pain syndrome, by 55.2% reducing trimeperidine consumption rate for the first 24 hours after the surgical intervention and by 20.3±1.4 hours earlier starting activation of patients if compared to the prolonged epidural analgesia

Resolution of a shock in hyperbolic systems modified by weak dispersion

We present a way to deal with dispersion-dominated ``shock-type'' transition in the absence of completely integrable structure for the systems that one may characterize as strictly hyperbolic regularized by a small amount of dispersion. The analysis is performed by assuming that, the dispersive shock transition between two different constant states can be modelled by an expansion fan solution of the associated modulation (Whitham) system for the short-wavelength nonlinear oscillations in the transition region (the so-called Gurevich -- Pitaevskii problem). We consider as single-wave so bi-directional systems. The main mathematical assumption is that of hyperbolicity of the Whitham system for the solutions of our interest. By using general properties of the Whitham averaging for a certain class of nonlinear dispersive systems and specific features of the Cauchy data prescription on characteristics we derive a set of transition conditions for the dispersive shock, actually bypassing full integration of the modulation equations. Along with model KdV and mKdV examples, we consider a non-integrable system describing fully nonlinear ion-acoustic waves in collisionless plasma. In all cases our transition conditions are in complete agreement with previous analytical and numerical results.Comment: 56 pages, 5 figures. Misprints corrected. References adde

Stable multicolor periodic-wave arrays

We study the existence and stability of cnoidal periodic wave arrays propagating in uniform quadratic nonlinear media and discover that they become completely stable above a threshold light intensity. To the best of our knowledge, this is the first example in physics of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons.Comment: 12 pages, 3 figure

Study of the influence of the electron irradiation dose on the deformation of Mylar films taking into account the processes of destruction and crosslinking

Experimental studies of the dependence of the deformation [epsilon] on the dose of electron irradiation D taking into account the processes of destruction and crosslinking for films of the Mylar type have been carried out. It was obtained that the dependence of [epsilon] on D for the process of cross-linking is described by a linear and destruction by an exponential function