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 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.

Integrable discretization of soliton equations via bilinear method and Backlund transformation

We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method.This approach is mainly based on the compatibility between an integrable system and its B¨acklund transformation.We apply this procedure to several equations,including the extended Korteweg-deVries(Kd V)equation,the extended Kadomtsev-Petviashvili(KP)equation,the extended Boussinesq equation,the extended Sawada-Kotera(SK)equation and the extended Ito equation,and obtain their associated semidiscrete analogues.In the continuum limit,these differential-difference systems converge to their corresponding smooth equations.For these new integrable systems,their B¨acklund transformations and Lax pairs are derived.

An Augmented Lagrangian based Semismooth Newton Method for a Class of Bilinear Programming Problems

This paper proposes a semismooth Newton method for a class of bilinear programming problems(BLPs)based on the augmented Lagrangian,in which the BLPs are reformulated as a system of nonlinear equations with original variables and Lagrange multipliers.Without strict complementarity,the convergence of the method is studied by means of theories of semismooth analysis under the linear independence constraint qualification and strong second order sufficient condition.At last,numerical results are reported to show the performance of the proposed method.

Soliton Solutions and Bilinear Bcklund Transformation for Generalized Nonlinear Schrdinger Equation with Radial Symmetry

Investigated in this paper is the generalized nonlinear Schrodinger equation with radial symmetry. With the help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method. B^cklund transformation in the bilinear form is presented, through which a new solution is constructed. Graphically, we have found that the solitons are symmetric about x = O, while the soliton pulse width and amplitude will change along with the distance and time during the propagation.

Dynamics of Nonlinear Waves in(2+1)-Dimensional Extended Boiti-Leon-Manna-Pempinelli Equation

Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.

High-Order Solitons and Hybrid Behavior of (3 + 1)-Dimensional Potential Yu-Toda-Sasa-Fukuyama Equation with Variable Coefficients

In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton (N=1,2) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions.

Fuzzy Varying Coefficient Bilinear Regression of Yield Series

We construct a fuzzy varying coefficient bilinear regression model to deal with the interval financial data and then adopt the least-squares method based on symmetric fuzzy number space. Firstly, we propose a varying coefficient model on the basis of the fuzzy bilinear regression model. Secondly, we develop the least-squares method according to the complete distance between fuzzy numbers to estimate the coefficients and test the adaptability of the proposed model by means of generalized likelihood ratio test with SSE composite index. Finally, mean square errors and mean absolutely errors are employed to evaluate and compare the fitting of fuzzy auto regression, fuzzy bilinear regression and fuzzy varying coefficient bilinear regression models, and also the forecasting of three models. Empirical analysis turns out that the proposed model has good fitting and forecasting accuracy with regard to other regression models for the capital market.

广义地球物理KdV方程的Lump波与扭结波相互作用解初值扰动行为

针对一类广义地球物理KdV方程进行研究,利用Painleve分析思想构造了一个包含初始常数解的双线性变换,并应用拟设函数法得到两类与初值有关的Lump波与周期波、扭结波相互作用的显式精确解.此外,根据包含初始常数解u 0扰动的解的结构得到u 0的两个分叉点.最后,在一定参数条件下,利用数学软件对所得Lump波与周期波相互作用模式、Lump波与扭结波相互作用模式进行了绘图展示.结果表明:方程初始常数解对广义地球物理KdV方程的发展性态具有明显的扰动特征.

(3+1)维Hirota双线性方程的lump解

非线性发展方程是现代数学的一重要分支,其精确解的计算一直都是非线性科学领域的主流与焦点问题.lump解是精确解析解的一种特殊形式,以(3+1)维Hirota双线性方程为例对此展开研究.首先,利用Hirota双线性方法研究其经典lump解.其次,以双线性神经网络方法为基础,借助符号计算方法,得到方程的高阶lump解,主要是4阶lump解的计算.最后,通过对参数赋予一些特殊值,借助Maple软件,绘制出相关的三维图、密度图、相图以及传播图等,得到一些新的现象,同时展示了所求出的解的动力学行为.

(3+1)维广义非线性发展方程的双线性Backlund变换与精确解

基于Hirota双线性方法和试探函数法,研究一个(3+1)维广义非线性发展方程的双线性Backlund变换和精确解问题。用Hirota双线性法,构造(3+1)维广义非线性发展方程的双线性形式和双线性Backlund变换。基于双线性形式和双线性Backlund变换,利用试探函数法与符号计算系统Mathematica,获得(3+1)维广义非线性发展方程的多种精确解,包括呼吸波解、复合型解、Lump周期解和孤子解,并分析解的相互作用情况。

试样厚度对小冲杆试验力与材料强度相关性的影响

为了研究试样厚度对小冲杆试验力与材料强度相关性的影响,针对不同厚度(0.1~0.5 mm)的小冲杆试样,使用无屈服平台的虚拟材料进行了有限元模拟。通过提取并分析有限元模拟结果中固定挠度下的小冲杆试验力,证明了小冲杆试验力与材料屈服强度和抗拉强度的双线性关系,且厚度的变化不会影响该相关关系的皮尔逊相关系数。随机生成了屈强比在0.55~0.9之间,屈服强度在200~1000 MPa之间的100种虚拟材料,并通过有限元模拟获得了大量数据,进而采用退火粒子群算法得出了固定挠度下小冲杆试验力和材料强度的关联系数。采用4种真实材料验证了小冲杆试验力与材料强度呈双线性关系的结论。

(1+1)维的具有时间与空间色散的五阶方程

研究了一个新的(1+1)维的具有时空色散可积五阶方程,推广了方程的形式,并探讨了色散关系及其各自的系数情况.利用简化Hirota方法推导了方程的可积条件,导出了多孤子解.此外,利用指数型初始解构造方程的变换,得出双线性方程,继而利用Hirota双线性导数法导出单孤子解、双孤子解及N孤子解.结合双线性方程给出了不同双线性交换算子的双线性Bäcklund变换,继而导出不同条件下的双曲行波解、周期行波解等行波解.

三参数威布尔分布参数估计方法比较

选择目前常用的5种三参数威布尔分布参数估计法(概率权重矩法、极大似然法、双线性回归法、相关系数优化法、灰色估计法)进行比较研究,采用不同样本的7组数据进行参数估计,得出了这5种方法各自相应的适用范围,相关结论对正确选用三参数威布尔分布参数求解方法有一定指导意义.

(2+1)维非线性Schrdinger型方程的同宿轨道

研究了几类(2+1)维非线性Schrdinger型方程同宿轨道的问题.利用Hirota双线性算子方法,通过给出的相关变换,得到了包括(2+1)维的长短波相互作用方程,广义Zakharov方程,Mel’nikov方程和g-Schrdinger方程的同宿轨道解的显式解析表达式,从而讨论了这些方程的同宿轨道.

体外CFRP筋预应力混凝土箱梁长期受力性能试验研究

碳纤维(CFRP)筋具有优异的物理力学性能,可用于替代传统的预应力钢筋。制作了体外配置碳纤维筋预应力混凝土箱梁模型,对持续均布荷载作用箱梁的截面应力重分布、长期挠曲变形及裂缝发展等规律进行了1001 d的试验观测。基于素混凝土柱体的实测徐变系数,运用双线性法和曲率法分别对试验箱梁的长期挠曲变形进行预测。试验结果表明:受压钢筋应变较初值增长225%～268%,受拉钢筋的应变较初值增长36.2～38.6%,混凝土表面压应变较初值增长164%～224%。按现行设计规范计算长期荷载作用特征裂缝宽度较实测值偏小11.8%～55.5%。跨中长期挠曲变形实测值为初始变形的2.32～2.42倍,较现行设计规范取值偏大18.5%。

盐渍土溶陷特性的试验研究与分析

本文以新疆（北疆）地区S201线克拉玛依至榆树沟段公路沿线的盐渍土为研究对象，着重对该土的溶陷特性进行了试验研究，目的是为新疆的公路设计和施工提供合理的技术指导。运用单轴压缩试验，通过利用单、双线法试验结果的对比分析，总结出了盐渍土的溶陷变形随含水量和压力变化的规律及特点。研究认为：对于不同类型的盐渍土，不论采用何种试验方法，都会得到溶陷系数、峰值溶陷压力随含水量增大而减小，氯盐盐渍土峰值溶陷压力在400—500kPa附近，而硫酸盐盐渍土峰值溶陷压力在200kPa附近；同时还得出不同类型的盐渍土对水的敏感程度相同，即试验开始与结束表现为敏感弱，而中间阶段表现较强；从试验方法符合实际情况以及结果准确入手，双线法比单线法更适合于对盐渍土溶陷性的试验研究。

典型浓度路径(RCP)情景下长江中下游地区气温变化预估

为探明典型浓度路径下(高端路径RCP8.5和稳定路径RCP4.5)长江中下游地区未来30a平均气温的时空变化趋势和分布特征,运用联合国政府间气候变化委员会(IPCC)AR5提出的模拟能力较强的BCC-CSM1-1(Beijing Climate Center Climate System Model version1-1)气候系统模式,基于典型浓度情景RCP(Representative Concentration Pathway)输出的2021-2050年0.5×0.5格点主要气象要素的逐日模式模拟数据资料,应用双线性内插法降尺度到长江中下游及邻近区域62个基本气象站点。以1961-1990为基准年,根据同期等长模拟数据和观测数据的非线性函数关系建立订正模型,并利用方差订正法对2021-2050年模拟数据进行误差订正。结果表明:RCP情景输出数据的模拟效果良好,方差订正可降低模拟值与观测值的相对误差和方差,更加真实反应未来气候变化趋势。RCP8.5和RCP4.5两种排放情景下,长江中下游地区2021-2050年年平均气温均呈显著上升趋势,增温幅度总体表现为自南向北逐渐减少。就季节而言,四季均呈现升温趋势,夏季增温幅度最高,变化倾向率大,春冬两季RCP8.5情景下增温幅度大于RCP4.5下,夏秋季则相反;RCP8.5情景下,研究区域年平均气温呈现自中部向东西递减,春夏季增温幅度高于秋季,冬季增温幅度最小,且变化倾向率低,大部分地区未通过0.05水平的显著性检验。RCP4.5情景下,研究区年平均气温自北向南逐渐降低,变化倾向率则表现为北部大于南部,夏季变化速率较大,增温幅度达1.2℃·10a^(-1)(P<0.01),冬季较小且未通过显著性检验。

两类(2+1)-维孤子方程的显式解

应用双线性方法,在(1+1)-维方程的帮助下,研究和讨论两类(2+1)-维孤子方程的显式解,给出了方程的单孤子解,双孤子解和N-孤子解,提供了求(2+1)-维孤子方程显式解的可行途径。