Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates
is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth’s magnetotail region.

Dissipative solitons in fiber lasers

Dissipative solitons (also known as auto-solitons) are stable, nonlinear, time-or space-localized solitary waves that occur due to the balance between energy excitation and dissipation. We review the theory of dissipative solitons applied to fiber laser systems. The discussion context includes the classical Ginzburg-Landau and Maxwell-Bloch equations and their modifications that allow describing laser-cavity-produced waves. Practical examples of laser systems generating dissipative solitons are discussed.

Finite time blow-up and breaking of solitary wind waves

The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg-de Vries-Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.

Stable periodic waves in coupled Kuramoto-Sivashinsky-Korteweg-de Vries equations

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky-Korteweg-de Vries (KS-KdV) equation linearly coupled to an extra linear dissipative one. The model describes, e.g., a two-layer liquid film flowing down an inclined plane. It has been recently shown that the system supports stable solitary pulses. We demonstrate that a perturbation analysis, based on the balance equation for the net field momentum, predicts the existence of stable cnoidal waves (CnWs) in the same system. It is found that the mean value u(0) of the wave field u in the main subsystem, but not the mean value of the extra field, affects the stability of the periodic waves. Three different areas can be distinguished inside the stability region in the parameter plane (L, u(0)), where L is the wave's period. In these areas, stable are, respectively, CnWs with positive velocity, constant solutions, and CnWs with negative velocity. Multistability, i.e., the coexistence of several attractors, including the waves with several maxima per period, appears at large value of L. The analytical predictions are completely confirmed by direct simulations. Stable waves are also found numerically in the limit of vanishing dispersion, when the KS-KdV equation goes over into the KS one.

Dissipative three-wave structures in stimulated backscattering. I. A subluminous solitary attractor

We present a solitary solution of the three-wave nonlinear partial differential equation (PDE) model - governing resonant space-time stimulated Brillouin or Raman backscattering - in the presence of a cw pump and dissipative material and Stokes waves. The study is motivated by pulse formation in optical fiber experiments. As a result of the instability any initial bounded Stokes signal is amplified and evolves to a subluminous backscattered Stokes pulse whose shape and velocity are uniquely determined by the damping coefficients and the cw-pump level. This asymptotically stable solitary three-wave structure is an attractor for any initial conditions in a compact support, in contrast to the known superluminous dissipative soliton solution which calls for an unbounded support. The linear asymptotic theory based on the Kolmogorov-Petrovskii-Piskunov assertion allows us to determine analytically the wave-front slope and the subluminous velocity, which are in remarkable agreement with the numerical computation of the nonlinear PDE model when the dynamics attains the asymptotic steady regime. © 1997 The American Physical Society.

Solitary wave behavior at concave barriers /

Mode of access: Internet.

Aspecto tumoral da cisticercose intracraniana: abordagem cirúrgica

The cerebral cysticercosis can produce intracranial hypertension by inflammatory obstruction of the basal cysterns or by expansive lesion in the cerebral parenchima or ventricular cavities. In the latter and in tumor cases the clinical picture is very similar and only after surgery can the etiology be determined. We present 11 operated cases of intracranial cysticercosis which presented the clinical picture of an expansive lesion. There were 7 females and 4 males with ages between 4 and 65 years. Nine patients were admitted because of headache, vomiting and visual disturbances suggestive of intracranial hypertension. One patient was admited with lymphocytic meningitis and another with focal seizures following hemiparesis. Five patients presented focal signs and six edema of the papilla. Epileptic manifestations were present in 45.5% of the cases. A plain X-ray films of the skull failed to reveal calcificatons, however signs of chronic hypertension were present in three cases. The electroencephalogram showed slow focal waves in 8 patients The spinal fluid examination revealed lymphocytosis in 4 cases, increased protein content in another 4 and complement fixation for cysticercosis was positive in 2 cases. The expansive lesions were localized by angiograph and ventriculography. In these the location was temporal in 4, frontal in 3, parietal in 2, in the third ventricle in one and in the fourth ventricle in another. At surgery we removed a large cyst from the cerebral parenchyma in six cases. Around the cyst a thick glial reaction was present. In the other cases the cyst was small but fixed to the ventricular trigone and produced dilatation of the inferior horn of the lateral ventricle. In two cases we removed a solitary intraventricular cyst from the third and fourth ventricles. In the two children operated upon there were several small hard cysts involving the cerebral parenchyma which displayed intense gliosis. There were no postoperative complications.

Phoretic mites (Acari: Chaetodactylidae) associated with the solitary bee Tetrapedia diversipes (Apidae: Tetrapediini)

Solitary bees of the genus Tetrapedia have a specific association with mites of the genus Roubikia (Chaetodactylidae). These mites are frequently found attached to active Tetrapedia bees. We quantified the number of mites on individuals of Tetrapedia diversipes Klug and examined the interaction between these species. Nests of T. diversipes were obtained from trap-nests placed in four localities in Sao Paulo, Brazil. The study lasted from March 2007 to February 2009. Out of a total of 650 nests with emergences, 118 were infested with mites (Roubikia sp.). From these nests, 176 individuals of T. diversipes emerged with mites on their bodies. Additionally, six individuals of Coelioxoides waltheriae, the specific kleptoparasitic bee to T. diversipes, emerged. Mites were attached mainly to the mesosoma. All nests infected with mites did not presented mortality of the immature. The mortality rate of nests was inversely related to the level of mite infestation, suggesting a mutualistic interaction in which mites may remove fungi from the nests, while the bees would provide the mites with transport, dispersal, and shelter.

Male sleeping aggregations of solitary oil-collecting bees in Brazil (Centridini, Tapinotaspidini, and Tetrapediini; Hymenoptera: Apidae)

Males of solitary bees usually spend the night in clusters on small branches of plants, cavities and flowers. The individuals usually return to the same location each evening during their life, exhibiting site fidelity to a particular plant. We report on the sleeping roosts of the males of some oil-collecting bees of the genera Centris, Paratetrapedia, Lanthanomelissa, Monoeca, and Tetrapedia, as well as the host plants. We discuss the role of the male clusters to the associated plants.

Reduction of chaotic particle transport driven by drift waves in sheared flows

Investigations of chaotic particle transport by drift waves propagating in the edge plasma of tokamaks with poloidal zonal flow are described. For large aspect ratio tokamaks, the influence of radial electric field profiles on convective cells and transport barriers, created by the nonlinear interaction between the poloidal flow and resonant waves, is investigated. For equilibria with edge shear flow, particle transport is seen to be reduced when the electric field shear is reversed. The transport reduction is attributed to the robust invariant tori that occur in nontwist Hamiltonian systems. This mechanism is proposed as an explanation for the transport reduction in Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao , Plasma Phys. Controlled Fusion 43, 1181 (2001)] for discharges with a biased electrode at the plasma edge.

Absorption of planar waves in a draining bathtub

We present an analysis of the absorption of acoustic waves by a black hole analogue in (2 + 1) dimensions generated by a fluid flow in a draining bathtub. We show that the low-frequency absorption length is equal to the acoustic hole circumference and that the high-frequency absorption length is 4 times the ergoregion radius. For intermediate values of the wave frequency, we compute the absorption length numerically and show that our results are in excellent agreement with the low-and high-frequency limits. We analyze the occurrence of superradiance, manifested as negative partial absorption lengths for corotating modes at low frequencies.

Scattering of massless scalar waves by Reissner-Nordstrom black holes

We present a study of scattering of massless planar scalar waves by a charged nonrotating black hole. Partial wave methods are applied to compute scattering and absorption cross sections, for a range of incident wavelengths. We compare our numerical results with semiclassical approximations from a geodesic analysis, and find excellent agreement. The glory in the backward direction is studied, and its properties are shown to be related to the properties of the photon orbit. The effects of the black hole charge upon scattering and absorption are examined in detail. As the charge of the black hole is increased, we find that the absorption cross section decreases, and the angular width of the interference fringes of the scattering cross section at large angles increases. In particular, the glory spot in the backward direction becomes wider. We interpret these effects under the light of our geodesic analysis.

Scattering of sound waves by a canonical acoustic hole

This is a study of a monochromatic planar perturbation impinging upon a canonical acoustic hole. We show that acoustic hole scattering shares key features with black hole scattering. The interference of wave fronts passing in opposite senses around the hole creates regular oscillations in the scattered intensity. We examine this effect by applying a partial wave method to compute the differential scattering cross section for a range of incident wavelengths. We demonstrate the existence of a scattering peak in the backward direction, known as the glory. We show that the glory created by the canonical acoustic hole is approximately 170 times less intense than the glory created by the Schwarzschild black hole, for equivalent horizon-to-wavelength ratios. We hope that direct experimental observations of such effects may be possible in the near future.