We report on a patient with a large, painful hypertrophic scar on the plantar aspect of the left foot who was treated with carbon dioxide laser and a skin substitute (Apligraf) and followed up for ...longer than 1 year. To our knowledge, no other case reports have been published on the use of a skin substitute to gain coverage and resolution after excision of a hypertrophic scar by carbon dioxide laser.
The anomalies observed at RHIC for the baryon — meson ratios have prompted a number of theoretical works on the nature of the hadrochemistry in the hadronisation stage of the pp collisions and in the ...evolution of the dense system formed in heavy ion collisions. Although the predictions differ in the theoretical approach, generally a substantial increase in the baryon production is predicted in the range 10–30 GeV/c. We will present the possibilities of a gas ring imaging Cherenkov detector of limited acceptance which would be able to identify track-by-track protons until 24 GeV/c for the ALICE experiment.
The fundamental concept of colored nonautonomous solitons in nonlinear and dispersive nonautonomous physical systems is introduced. Novel soliton solutions for the nonautonomous nonlinear Schrödinger ...equation models with linear and harmonic oscillator potentials substantially extend the concept of classical solitons and generalize it to the plethora of nonautonomous solitons that interact elastically and generally move with varying amplitudes, speeds and spectra adapted both to the external potentials and to the dispersion and nonlinearity variations. The parallels between nonlinear guided wave phenomena in optics and nonlinear guided wave phenomena in Bose condensates are clearly demonstrated by considering optical and matter wave soliton dynamics in the framework of nonautonomous evolution equations. The exact analytical solutions and numerical experiments reveal many specific features of nonautonomous solitons. Fundamental laws of the soliton adaptation to the external potentials are derived. Bound states of colored nonautonomous solitons are studied in detail and a comparison of the canonical Satsuma-Yajima breather dynamics with a nonautonomous 'agitated' breather is presented. The nonautonomous soliton concept can be applied to different physical systems, from hydrodynamics and plasma physics to nonlinear optics and matter waves, and offer many opportunities for further scientific studies
We introduce the concept of nonlinear optics of nuclear reactions and reveal a deep analogy between nonlinear dynamics of the so-called “well-dressed repulsive-core” solitons and the nuclear ...reactions that take place among atomic nuclei. We derive a nonlinear evolution equation for the Fermi nuclear density and the Woods–Saxon potential based on the inverse problem in the diffraction and dispersion scattering. We obtain a simple formula for the self-interaction (binding) energy, which provides the shape and structural stability of “soliton-like nucleus” with the Fermi density distribution. We find the shape squareness parameter (edge steepness) for “soliton-like nucleus” density distribution and demonstrate its specific quantization related to the conservation of the total number of nucleons. The shape squareness parameter plays a decisive role in increasing the binding soliton energy and appearing the oscillatory side-band spectral structures responsible for the fusion and fission reactions with soliton-like nuclei. We hope that nonlinear-optical analogies found in our work will be able to shed additional light on the fundamental problems of stellar nucleosynthesis. We support our findings with concrete examples of fusion and fission reactions with “well-dressed repulsive-core” nucleus-like solitons: the carbon and oxygen-burning processes, the iron-synthesis, and nuclear fusion–fission reactions induced by alpha particles.
Novel soliton solutions for the nonautonomous nonlinear Schrödinger equation models with linear and harmonic oscillator potentials substantially extend the concept of classical solitons and ...generalize it to the plethora of nonautonomous solitons that interact elastically and generally move with varying amplitudes, speeds, and spectra adapted both to the external potentials and to the dispersion and nonlinearity variations. The nonautonomous soliton concept can be applied to different physical systems, from hydrodynamics and plasma physics to nonlinear optics and matter waves, and offer many opportunities for further scientific studies.
We apply the method for systematic construction of the two-soliton (and in principal, N-soliton) breather solutions on the zero background to the Lakshmanan–Porsezian–Daniel model with varying ...dispersion and nonlinearity, gain or loss, and derive the specific conditions for the appearance of the so-called standing and moving soliton breathers. We show that both all parameters of constituent solitons forming the breather and the varying dispersion and nonlinearities should be appropriately chosen in accordance with the exact integrability conditions of the Lakshmanan–Porsezian–Daniel equation with vanishing boundary conditions. We compare the details of periodic breather dynamics for the complex modified KdV, Hirota, and Lakshmanan–Porsezian–Daniel models with the classical Satsuma–Yajima breather behavior. We derive simple formulas for the soliton breather periods and use them to understand the possibilities to control breather dynamics, and, in particular, to realize the so-called regimes of “artificial breathing”, when periods of soliton breathing in space and time are controlled by choosing appropriate complex spectral parameters defining the amplitudes and velocities of constituent solitons. Of fundamental importance is the remarkable theoretical fact that the higher-order nonlinear and dispersion effects included into (or removed from) the new higher-order equations of the AKNS hierarchy, as a rule, do not destroy soliton breathers discovered here and do not transform them into dispersive waves. On the contrary, we demonstrate that novel and novel soliton breathers can appear in the framework of the next, more and more higher orders of the AKNS and NLSE hierarchies.
By means of analytical and numerical methods, we reveal the main features of nonautonomous matter-wave solitons near the Feshbach resonance in a one-dimensional Bose-Einstein condensate confined by a ...harmonic potential with a varying-in-time longitudinal trapping frequency. Based on the generalized nonautonomous Gross-Pitaevskii model, we show that solitons in nonautonomous physical systems exist only under certain conditions so that varying-in-time nonlinearity and confining harmonic potential cannot be chosen independently; they satisfy the exact integrability scenarios and complement each other. We focus on the most physically important examples where the applied magnetic field is either a linearly or a periodically varying-in-time function. In the case of periodically varying scattering length, variations of confining harmonic potential are found to be sign-reversible (periodic attractive and repulsive) to support the soliton-management regime. We investigate the losses of validity of one-dimensional (1D) approximation in the cases when, by the joint action of varying-in-time nonlinearity and confining potential, the atom cloud can be compressed from an initially elongated quasi-1D cigar-shaped geometry to a final ball-shaped three-dimensional geometry and the induced soliton collapse may occur.
We reveal that external potentials in completely integrable higher-order nonautonomous nonlinear dynamical systems can be expressed as an infinite power series with time-varying coefficients. As the ...representative example, the generalized Hirota equation is introduced in this work in the framework of the nonisospectral generalization of the Inverse Scattering Transform method with associated spectral parameter varying in accordance with the Riccati equation. We demonstrate that accelerating and self-compressing nonautonomous solitons of the introduced model conserve the soliton main feature to interact elastically both in the linear, parabolic, and cubic external potentials, and are controlled only if the varying dispersion and nonlinearity satisfy to the conditions of the exact integrability.
