Transverse instability in nonparaxial systems with four-wave mixing.

We present a two-dimensional coupled nonlinear Schrödinger-like system with spatial diffractions, degree of birefringence, and four-wave mixing. This system describes two physical contexts: optical pulse propagation beyond the paraxial approximation in a weakly birefringence waveguide and light propagation near exciton-polariton resonance in semiconductor superlattice materials. We find that such systems naturally support different types of diffraction profiles, including spherical, ellipsoidal, and hyperbolic structures. We then study the transverse instability of the two-dimensional system caused by an infinitesimal perturbation-induced continuous-wave solution. Also, we find out how various physical parameters, such as nonparaxiality, degree of birefringence, power, and four-wave mixing, affect the modulational instability (MI) process, in particular. We explore the existence of bright solitary wave solutions for the proposed system as the influence of MI is closely related to the latter in a nutshell.

Cubic-quintic nonlinear Helmholtz equation: Modulational instability, chirped elliptic and solitary waves.

We study the formation and propagation of chirped elliptic and solitary waves in the cubic-quintic nonlinear Helmholtz equation. This system describes nonparaxial pulse propagation in a planar waveguide with Kerr-like and quintic nonlinearities along with spatial dispersion originating from the nonparaxial effect that becomes dominant when the conventional slowly varying envelope approximation fails. We first carry out the modulational instability (MI) analysis of a plane wave in this system by employing the linear stability analysis and investigate the influence of different physical parameters on the MI gain spectra. In particular, we show that the nonparaxial parameter suppresses the conventional MI gain spectrum and also leads to a nontrivial monotonic increase in the gain spectrum near the tails of the conventional MI band, a qualitatively distinct behavior from the standard nonlinear Schrödinger system. We then study the MI dynamics by direct numerical simulations, which demonstrate the production of ultrashort nonparaxial pulse trains with internal oscillations and slight distortions at the wings. Following the MI dynamics, we obtain exact elliptic and solitary wave solutions using the integration method by considering physically interesting chirped traveling wave ansatz. In particular, we show that the system features intriguing chirped antidark, bright, gray, and dark solitary waves depending upon the nature of nonlinearities. We also show that the chirping is inversely proportional to the intensity of the optical wave. In particular, the bright and dark solitary waves exhibit unusual chirping behavior, which will have applications in the nonlinear pulse compression process.

Development of a core outcome set for epilepsy in pregnancy (E-CORE): a national multi-stakeholder modified Delphi consensus study.

OBJECTIVE: To develop a set of core outcomes for studies on pregnant women with epilepsy. DESIGN: Delphi consensus study. POPULATION: Healthcare professionals, and patient representatives with lived experience of epilepsy in the UK. METHODS: We used a modified Delphi method and a consultation meeting to achieve consensus. Potential outcomes were identified by systematic review, and were scored using a Likert scale anchored between 1 (least important) and 5 (most important). We included outcomes that scored ≥4 by >70% of participants, and outcomes that scored ≤2 by <15% of participants. MAIN OUTCOME MEASURES: Outcomes in studies on epilepsy in pregnancy. RESULTS: Seventy-five healthcare professionals completed the first round, 48 (64%) completed the second round, and 37 (49%) completed the third round of the survey. Twenty-four patient representatives participated. The final core outcome set included 31 outcomes in three domains: neurological, offspring, and obstetric. Outcomes in the neurological domain were seizure control in pregnancy and postpartum, status epilepticus, maternal mortality, drowning, sudden unexpected death in epilepsy, postnatal depression, and quality of life. Offspring domain included congenital abnormalities (major and minor), fetal anticonvulsant syndrome, neurodevelopment, autism disorder, neonatal clinical complications, admission to a neonatal intensive care unit, and anthropometric measurements. The obstetric domain included live birth, stillbirth, miscarriage, ectopic, termination of pregnancy, admission to a high dependency or intensive care unit, breastfeeding, mode of delivery, preterm birth, pre-eclampsia, and eclampsia. Outcomes specific for studies on anti-epileptic drugs (AEDs) included maternal AED toxicity, AED compliance, neonatal withdrawal symptoms, and neonatal haemorrhagic disease. CONCLUSION: Embedding this core set in future clinical trials will promote the standardisation of reporting to inform clinical practice. TWEETABLE ABSTRACT: A Delphi method identifying core outcomes for epilepsy in pregnancy. Final core set includes 31 outcomes.

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.