Soliton Solutions of Coupled KdV System from Hirota's Bilinear Direct Method

With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.

The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq-Burgers equation

This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton） solutions and multiple-singular-kink （soliton） solutions are derived for the two equations.

Soliton Solutions for Nonisospectral AKNS Equation by Hirota＇s Method

Bilinear form of the nonisospectral AKNS equation is given. The N-soliton solutions are obtained through Hirota＇s method.

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

The forecasting efficiency under different selected regions by Pattern Informatics Method and seismic potential estimation in the North-South Seismic Zone

In 2022,four earthquakes with M_(S)≥6.0 including the Menyuan M_(S)6.9 and Luding M_(S)6.8 earthquakes occurred in the North-South Seismic Zone(NSSZ),which demonstrated high and strong seismicity.Pattern Informatics(PI)method,as an effective long and medium term earthquake forecasting method,has been applied to the strong earthquake forecasting in Chinese mainland and results have shown the positive performance.The earthquake catalog with magnitude above M_(S)3.0 since 1970 provided by China Earthquake Networks Center was employed in this study and the Receiver Operating Characteristic(ROC)method was applied to test the forecasting efficiency of the PI method in each selected region related to the North-South Seismic Zone systematically.Based on this,we selected the area with the best ROC testing result and analyzed the evolution process of the PI hotspot map reflecting the small seismic activity pattern prior to the Menyuan M_(S)6.9 and Luding M_(S)6.8 earthquakes.A“forward”forecast for the area was carried out to assess seismic risk.The study shows the following.1)PI forecasting has higher forecasting efficiency in the selected study region where the difference of seismicity in any place of the region is smaller.2)In areas with smaller differences of seismicity,the activity pattern of small earthquakes prior to the Menyuan M_(S)6.9 and Luding M_(S)6.8 earthquakes can be obtained by analyzing the spatio-temporal evolution process of the PI hotspot map.3)The hotspot evolution in and around the southern Tazang fault in the study area is similar to that prior to the strong earthquakes,which suggests the possible seismic hazard in the future.This study could provide some ideas to the seismic hazard assessment in other regions with high seismicity,such as Japan,Californi,Turkey,and Indonesia.

A Simplified Hirota Method and Its Application

By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.

Research on the Application of Montessori Education Method in Cognitive Training of Patients with Alzheimer’s Disease

Objective:To study the application of the Montessori education method in cognitive training in patients with Alzheimer’s disease(AD).Methods:40 cases of senile dementia patients who were admitted to our hospital from January 2022 to January 2023 were selected and randomly divided into an intervention group and a control group according to the single and double number table method,with 20 cases in each group.The intervention group used the Montessori education method,the principle of which was to implement individualized health interventions based on the individual conditions of the patients,for a period of 6 months;the control group was given conventional treatment and nursing of the disease.The Mini-Mental State Examination(MMSE)was used to compare the effects of the two groups of patients before and after health intervention and conduct statistical analysis.Results:The score of the intervention group was higher than that of the control group,and there was a statistical difference between the two(P<0.05).Conclusion:Implementing the Montessori education method for diagnosed Alzheimer’s patients can effectively improve their cognitive function and delay the progress of further dementia.

Solid Waste Management:A MADM Approach Using Fuzzy Parameterized Possibility Single-Valued Neutrosophic Hypersoft Expert Settings

The dramatic rise in the number of people living in cities has made many environmental and social problems worse.The search for a productive method for disposing of solid waste is the most notable of these problems.Many scholars have referred to it as a fuzzy multi-attribute or multi-criteria decision-making problem using various fuzzy set-like approaches because of the inclusion of criteria and anticipated ambiguity.The goal of the current study is to use an innovative methodology to address the expected uncertainties in the problem of solid waste site selection.The characteristics(or sub-attributes)that decision-makers select and the degree of approximation they accept for various options can both be indicators of these uncertainties.To tackle these problems,a novel mathematical structure known as the fuzzy parameterized possibility single valued neutrosophic hypersoft expert set(ρˆ-set),which is initially described,is integrated with a modified version of Sanchez’s method.Following this,an intelligent algorithm is suggested.The steps of the suggested algorithm are explained with an example that explains itself.The compatibility of solid waste management sites and systems is discussed,and rankings are established along with detailed justifications for their viability.This study’s strengths lie in its application of fuzzy parameterization and possibility grading to effectively handle the uncertainties embodied in the parameters’nature and alternative approximations,respectively.It uses specific mathematical formulations to compute the fuzzy parameterized degrees and possibility grades that are missing from the prior literature.It is simpler for the decisionmakers to look at each option separately because the decision is uncertain.Comparing the computed results,it is discovered that they are consistent and dependable because of their preferred properties.

Critical care nurses and their clinical reasoning for customizing monitor alarms:a mixed-method study

Objective:To explore the clinical rationale of critical care nurses for personalizing monitor alarms.One of the most crucial jobs assigned to critical care nurses is monitoring patients'physiological indicators and carrying out the necessary associated interventions.Successful use of equipment in the nursing practice environment will be improved by a thorough understanding of the nurse's approach to alarm configuration.Methods:A mixed-method design integrating quantitative and qualitative components was used.The sample of this study recruited a convenience sample of 60 nurses who have worked in critical care areas.This study took place at Lebanese American University Medical Center Rizk Hospital,utilizing a semi-structured interview with participants.Results:The study demonstrated the high incidence of nuisance alarms and the desensitization of critical care nurses to vital ones.According to the nurses,frequent false alarms and a shortage of staff are the 2 main causes of alarm desensitization.Age was significantly associated with the perception of Smart alarms,according to the data(P=0.03).Four interconnected themes and subcategories that reflect the clinical reasoning process for alarm customization were developed as a result of the study's qualitative component:(1)unit alarm environment;(2)nursing style;(3)motivation to customize;and(4)clinical and technological customization.Conclusions:According to this study,nurses believe that alarms are valuable.However,a qualitative analysis of the experiences revealed that customization has been severely limited since the healthcare team depends on nurses to complete these tasks independently.Additionally,a staffing shortage and lack of technical training at the start of placement have also hindered customization.

Homotopy Perturbation Method for the Generalized Hirota-Satsuma Coupled KdV Equation

In this paper, we consider the homotopy perturbation method (HPM) to obtain the exact solution of Hirota-Satsuma Coupled KdV equation. The results reveal that the proposed method is very effective and simple and can be applied to other nonlinear mathematical problems.

Hirota方法求解Boussinesq方程

利用Hirota方法求解(1+1)维和(2+1)维Boussinesq方程,得到其单孤立子解、双孤立子解以及N孤立子解的解析表达式,并通过数值模拟的方法展示了Boussinesq方程双孤子解的相互作用过程.

广义Hirota-Satsuma耦合KdV方程的精确解

利用(G'/G)-展开法结合数学软件Maple求得了广义Hirota-Satsuma耦合KdV方程的新精确解,包括孤波解、三角函数周期解和有理解.为了更直观地理解这些解,给出了它们的数值模拟图.

一般Hirota-Satsuma方程的多孤子解及孤子间的相互作用

用改进的齐次平衡法,首先把不可积的一般Hirota-Satsuma方程简化成可积模型—KdV方程,然后通过求解KdV方程得到了一般Hirota-Satsuma方程的多孤子解.利用得到的多孤子解分析了奇异孤子之间、钟型孤子与奇异孤子之间的相互作用,结果发现了相互作用的一些重要性质.

Hirota双线性导数变换与DNLS方程的孤子解

介绍并基于Hirota双线性导数变换，零边值条件下DNLS方程得以直接求解．其单孤子与双孤子解被作为两个典型特例以说明双线性导数变换法的一般应用手续．孤子之间的弹性碰撞通过双孤子情形得以展示，单孤子和双孤子解随时间与空间的演化也通过图表加以演示．

基于Hirota方法探求非零边界条件下MNLS/DNLS方程的孤子解

Hirota双线性导数变换处理非线性偏微分方程,是一种比反散射变换更为方便的直接方法。本文展示了Hirota双线性导数变换法应用于求解非线性可积方程的一般手续,以非零驻波边界条件下修正的非线性薛定谔(MNLS)方程为例,探求其孤子解;再通过简单的参数归零法直接得到导数非线性薛定谔(DNLS)方程在非零常数边界条件下的相应孤子解,亮/暗孤子解随时间和空间变量的演化也通过图像加以演示,所得孤子解与反散射方法得到的结果一致相符。

基于重排S-method的多分量辐射源信号分析方法

为实现多分量辐射源信号的有效检测和识别,提出了基于重排S-method(RSM)的多分量辐射源信号分析方法.针对Wigner-Ville分布交叉项严重和计算复杂度高的问题,采用RSM分析密集、交叠的辐射源信号,给出了其算法的硬件实现和计算复杂度分析.该方法能处理线性和非线性调频信号,算法简单,易于实现.复杂体制多分量辐射源信号分析的实验结果表明,该方法能有效分析多分量辐射源信号,时频分辨率高,不受交叉项干扰,具有比Wigner-Ville分布和S-method更强的噪声抑制能力.

基于S-method的多分量雷达辐射源信号检测

针对传统时频方法在处理多分量雷达辐射源信号时存在交叉项,不能检测各分量信号时域参数,难以适应低信噪比环境的问题,提出一种基于S-method(SM)的多分量雷达辐射源信号检测新方法。该方法首先计算信号的SM时频分布,然后在时频面的基础上检测各信号分量的瞬时频率和脉冲起止时间。实验结果表明,该方法能处理线性及非线性调频信号、时频分辨率高且不受交叉项干扰,时域检测精度大于98.60%,频域检测精度大于99.48%,信噪比降低时仍然保持强检测能力。

Comparative Analysis of Improving Effects of 12 Maize Populations with Improved S_1 Selection Method

ln this study, 12 maize populations were improved with the improved S1 selection method, aiming to increase the improvement efficiency of maize popula-tions. The results showed that number of rows per spike, number of grains per row and 100-grain weight were the three important component traits of maize yield. The highest genetic increment was found in Mengqun 2, fol owed by Mengqun 4, Mengqun 1 and other 7 maize populations. Negative genetic increment was shown in Mengqun 3 and 3 introduced foreign maize populations. Some changes were shown in spikes, plant traits and genetic diversity of maize populations. Based on our results, we concluded that Mengqun 2, Mengqun 4, Zhongzong 7, Mengqun C and Mengqun A could be directly used for the line breeding by selfing for their higher genetic increment of yield and better improvement effects of other agricultural traits. Compared with these 5 populations, the improvement potential of other maize populations was limited for their lower genetic increment.

广义耦合Hirota-Satsuma KdV方程组的对称约化和精确解

利用修正的CK直接方法,得到广义耦合Hirota-Satsuma KdV方程组的经典李点对称,并利用对称得到该方程的一些相似约化和新的精确解,同时,建立了该方程组的新、旧解之间的关系,从而推广了本文所得的新解.