Vector Soliton in Coupled Nonlinear Schrödinger Equation

Abstract Researchers are currently interested in studying the dynamics of the wave field in a nonlinear and dispersive medium. The Nonlinear Schrödinger Equation (NLSE), which is the fundamental equation that explains the phenomenon, has paved the way for research in a variety of fields, including soliton scattering. However, if the fields have a large number of components, the Coupled NLSE should be considered. We used orthogonally polarised and equal-amplitude vector solitons with two polarization directions to model the interactions. The effect of vector soliton scattering by external Delta potential in Coupled NLSE was studied in this paper. The scattering process is primarily determined by the initial velocity, amplitude of the soliton and potential strength. The variational approximation and direct numerical methods of Coupled NLSE were used to investigate the scattering process. The variational approximation (VA) method was used to analyse the dynamics of soliton’s width and center of mass position. The soliton may thus be reflected, transmitted or trapped within the potential. Uncoupled solitons may initially create a coupled state if their kinetic energy is less than the attractive interaction potential between solitons, but once their velocity surpasses the critical velocity, the soliton will easily pass through each other. To validate the approximation, a direct numerical simulation of CNLSE was performed. The results of the VA method and direct numerical simulation of Coupled NLSE are in good agreement when the parameters for both solutions are set to the same value. The initial velocity, potential strength and soliton amplitude play a role in the scattering of the vector soliton with Delta potential.</jats:p

Interactions of Soliton in Weakly Nonlocal Nonlinear Media

Abstract Solitary waves or solitons is a nonlinear phenomenon which has been studied intensively due to its application in solid-state matter such as Bose-Einstein condensates state, plasma physics, optical fibers and nematic liquid crystal. In particular, the study of nonlinear phenomena occurs in the structure of waves gained interest of scholars since their discovery by John Russell in 1844. The Nonlinear Schrödinger Equation (NLSE) is the theoretical framework for the investigation of nonlinear pulse propagation in optical fibers. Nonlocality can be found in an underlying transport mechanisms or long-range forces like electrostatic interactions in liquid crystals and many-body interactions with matter waves in Bose-Einstein condensate or plasma waves. The length of optical beam width and length of response function are used to classify nonlocality in optical materials. The nonlocality can be categorized as weak nonlocal if the width of the optical beam broader than the length of response function and if the width of the optical beam is narrower than the length of response function, it is considered as highly nonlocal. This work investigates the interactions of solitons in a weakly nonlocal Cubic NLSE with Gaussian external potential. The variational approximation (VA) method was employed to solve non integrable NLSE to ordinary differential equation (ODE). The soliton parameters and the computational program are used to simulate the propagation of the soliton width and its center-of-mass position. In the presence of Gaussian external potential, the soliton may be transmitted, reflected or trapped based on the critical velocity and potential strength. Direct numerical simulation of Cubic NLSE is programmed to verify the results of approximation method. Good agreement is achieved between the direct numerical solution and VA method results.</jats:p

F-18-FIBT may expand PET for beta-amyloid imaging in neurodegenerative diseases

F-18-FIBT, 2-(p-Methylaminophenyl)-7-(2-[F-18]fluoroethoxy)imidazo-[2,1-b]benzothiazole, is a new selective PET tracer under clinical investigation to specifically image beta-amyloid depositions (A beta) in humans in-vivo that binds to A beta with excellent affinity (K(d)0.7 +/- 0.2) and high selectivity over tau and alpha-synuclein aggregates (Ki > 1000 nM). We aimed to characterize(18)F-FIBT in a series of patients with different clinical-pathophysiological phenotypes and to compare its binding characteristics to the reference compound PiB. Six patients (mild late-onset and moderate early-onset AD dementia, mild cognitive impairment due to AD, intermediate likelihood, mild behavioral variant of frontotemporal dementia, subjective memory impairment without evidence of neurodegeneration, and mild dementia due to Posterior Cortical Atrophy) underwent PET imaging with(18)F-FIBT on PET/MR. With the guidance of MRI, PET images were corrected for partial volume effect, time-activity curves (TACs) of regions of interest (ROIs) were extracted, and non-displaceable binding potentials (BPnd), standardized uptake value ratios (SUVR), and distribution volume ratio (DVR) were compared. Specific binding was detected in the cases with evidence of the AD pathophysiological process visualized in images of BPnd, DVR and SUVR, consistently with patterns of different tracers in previous studies. SUVR showed the highest correlation with clinical severity. The previous preclinical characterization and the results of this case series suggest the clinical usefulness of FIBT as a selective and highly affine next-generation(18)F-labeled tracer for amyloid-imaging with excellent pharmacokinetics in the diagnosis of neurodegenerative diseases. The results compare well to the gold standard PiB and hence support further investigation in larger human samples

F-18-FIBT may expand PET for beta-amyloid imaging in neurodegenerative diseases (vol 25, pg 2608, 2020)

The author listing has been updated to indicate that Timo Grimmer and Kuangyu Shi are equally contributing authors