Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrodinger equation with sextic operator under non-zero boundary conditions

We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.

Riemann–Hilbert problem for the defocusing Lakshmanan–Porsezian–Daniel equation with fully asymmetric nonzero boundary conditions

The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.

Optimization of COVID-19 prevention and control measures during the Beijing 2022 Winter Olympics:a model-based study

Background:The continuous mutation of severe acute respiratory syndrome coronavirus 2 has made the coronavirus disease 2019(COVID-19)pandemic complicated to predict and posed a severe challenge to the Beijing 2022Winter Olympics and Winter Paralympics held in February and March 2022.Methods:During the preparations for the Beijing 2022 Winter Olympics,we established a dynamic model with pulsedetection and isolation efect to evaluate the efect of epidemic prevention and control measures such as entry policies,contact reduction,nucleic acid testing,tracking,isolation,and health monitoring in a closed-loop managementenvironment,by simulating the transmission dynamics in assumed scenarios.We also compared the importance ofeach parameter in the combination of intervention measures through sensitivity analysis.Results:At the assumed baseline levels,the peak of the epidemic reached on the 57th day.During the simulationperiod(100 days),13,382 people infected COVID-19.The mean and peak values of hospitalized cases were 2650and 6746,respectively.The simulation and sensitivity analysis showed that:(1)the most important measures to stopCOVID-19 transmission during the event were daily nucleic acid testing,reducing contact among people,and dailyhealth monitoring,with cumulative infections at 0.04%,0.14%,and 14.92%of baseline levels,respectively(2)strictlyimplementing the entry policy and reducing the number of cases entering the closed-loop system could delay thepeak of the epidemic by 9 days and provide time for medical resources to be mobilized;(3)the risk of environmentaltransmission was low.Conclusions:Comprehensive measures under certain scenarios such as reducing contact,nucleic acid testing,health monitoring,and timely tracking and isolation could efectively prevent virus transmission.Our research resultsprovided an important reference for formulating prevention and control measures during the Winter Olympics,andno epidemic spread in the closed-loop during the games indirectly proved the rationality of our research results.