Embed-Solitons and Their Evolutional Behaviors of (3+1)-Dimensional Burgers System

With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based onthe derived exact solutions, some novel and interesting localized coherent excitations such as embed-solitons are revealedby selecting appropriate boundary conditions and/or initial qualifications.The time evolutional properties of the novellocalized excitation are also briefly investigated.

Rational Solutions in a Coupled Burgers System

一个新联合汉堡包系统的合理解决方案的三种类型一以减小和 decoupled 过程详细再学习。合理答案的开始的二种类型为模型参数 c 的一种类型单个、有效 > 0，并且合理答案的另一种类型在任何类型是非退化的并且为模型参数 c 的另一种类型有效 < 0。

New Exact Solution of （N＋1）-Dimensional Burgers System

In this letter, using a Backlund transformation and the new variable separation approach, we find a new general solution of the (N+1)-dimensional Burgers system. The form of the universal formula obtained from many(2+1)-dimensional system is extended.

Exact Solutions of a Coupled Burgers System

一个新联合汉堡包系统的准确答案以三个不同方法被学习。解决方案的第一种类型由于拥有简单单个汉堡包减小的联合汉堡包系统被发现。多重 soliton 答案的第二种类型经由 decouple 过程被揭示。准确答案的第三种类型借助于热传导方程的 prioransatz 和答案被发现。模型的 soliton 分裂现象的二种不同类型被发现，没有模型的阶段移动的完全有弹性的 soliton 碰撞的一种特殊类型也被显示。

Variable Separation Approach to Solve （2 ＋ 1）-Dimensional Generalized Burgers System： Solitary Wave and Jacobi Periodic Wave Excitations

By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons,and previously revealed chaotic and fractal localized solutions, some new types of excitations compacton and dacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.

Continuous feedback control of KdV Burgers system

The chaos in the KdV Burgers equation describing a ferroelectric system has been successfully controlled by using a continuous feedback control. This system has two stationaxy points. In order to know whether the chaos is controlled or not, the instability of control equation has been analysed numerically. The numerical analysis shows that the chaos can be converted to one point by using one control signal, however, it can converted to the other point by using three control signals. The chaotic motion is converted to two desired stationary points and periodic orbits in numerical experiment sepaxately.

Embedded-Soliton and Complex Wave Excitations of (3+1)-Dimensional Burgers System

从扩大印射的途径和一个线性可变分离方法开始，我们与一些任意的函数发现可变分离解决方案的新家庭为(3+1 ) 维的汉堡包系统。然后基于象 embedded-solitons 那样的导出的准确答案，某小说和有趣的局部性的协调刺激，象逐渐变细一样 soliton，在周期的波浪背景的复杂波浪刺激被介绍适当边界条件或起始的资格揭示。复杂波浪刺激的进化性质简短被调查。

New Exact Solutions and Localized Structures for (3+1)-Dimensional Burgers System

与一条扩大印射的途径和一个线性可变分离方法，有任意的函数为的可变分离解决方案(包括的独居的波浪解决方案，周期的波浪解决方案，和合理函数解决方案) 的新家庭(3+1 ) 维的汉堡包系统被导出。基于导出的刺激，我们获得一些新奇局部性的协调结构并且学习在 solitons 之间的相互作用。

Non-Traveling Wave Solutions for the (1 + 1)-Dimensional Burgers System by Riccati Equation Mapping Approach

Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.

一种风向监督双流神经网络--以一维Burgers方程求解为例

针对一维Burgers方程下单一建模方式难以充分考虑不同阶段风向对系数的影响比重,无法有效获得各节点间的关联信息的问题,本文提出了一种风向监督双流神经网络分别预测上下风向的有限差分系数。同时设计了一种风向判断模块,实现了对预测得到有限差分系数的权重融合。通过风向监督双流神经网络,并结合先验知识对学得的系数分配一定的权重,以突出上下风向对预测结果的不同影响,可以有效实现对不同风向上的点分别进行预测,使得空间结构特征信息挖掘更加充分,从而提高差分系数预测的精度。在比传统数值求解方法网格分辨率粗4~8倍的同时,提高了谷歌团队工作的精度,以此提高了计算的速度。

定常Burgers方程的周期解

本文首先对Burgers方程的周期解关于粘性系数ε作幂级数展开,得到逼近函数之间的递推关系。然后,通过对逼近函数作Fourier级数展开,给出了逼近函数Fourier展开的通项形式,并证明了每个逼近函数的Fourier级数是一致且绝对收敛的。

Evolutionary dynamics of solitary wave profiles and abundant analytical solutions to a(3+1)-dimensional burgers system in ocean physics and hydrodynamics

In the fields of oceanography,hydrodynamics,and marine engineering,many mathematicians and physi-cists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenom-ena,one of which is a(3+1)-dimensional Burgers system that is currently being studied.In this paper,we apply two different analytical methods,namely the generalized Kudryashov(GK)method,and the generalized exponential rational function method,to derive abundant novel analytic exact solitary wave solutions,including multi-wave solitons,multi-wave peakon solitons,kink-wave profiles,stripe solitons,wave-wave interaction profiles,and periodic oscillating wave profiles for a(3+1)-dimensional Burgers sys-tem with the assistance of symbolic computation.By employing the generalized Kudryashov method,we obtain some new families of exact solitary wave solutions for the Burgers system.Further,we applied the generalized exponential rational function method to obtain a large number of soliton solutions in the forms of trigonometric and hyperbolic function solutions,exponential rational function solutions,peri-odic breather-wave soliton solutions,dark and bright solitons,singular periodic oscillating wave soliton solutions,and complex multi-wave solutions under various family cases.Based on soft computing via Wolfram Mathematica,all the newly established solutions are verified by back substituting them into the considered Burgers system.Eventually,the dynamical behaviors of some established results are exhibited graphically through three-and two-dimensional wave profiles via numerical simulation.

基于有限差分-谱方法的分数阶Burgers流体的非稳态驻点流动

研究了分数阶Burgers流体通过拉伸平板的非稳态驻点流动问题。将分数阶导数引入Burgers流体模型可以更好地模拟流动过程,但也增加了模型的复杂性和求解难度。首次运用有限差分-谱方法求解分数阶Burgers流体模型,离散格式构造简单有效。采用谱方法对控制方程中的空间项进行离散,利用有限差分方法分别结合L-1和L-2算法离散控制方程中的时间项,给出了两种离散格式,并且通过构造数值算例证明了离散格式的收敛性。结果表明,在靠近平板处,速度随着分数阶导数的增加而减小,而无穷远处的流体速度呈现出相反的趋势,体现了分数阶导数的记忆特性。此外,雷诺数越小,流体的粘度越大,导致流体速度越大。由于松弛时间参数的松弛特性,靠近平板处松弛时间参数对速度分布有抑制作用,远离平板处松弛时间促进流体流动。

一类非线性Burgers型问题的预测校正紧差分方法

针对一类非线性Burgers型方程,提出一种预测-校正紧差分方法。首先,对时间一阶导数采用一阶Euler格式,时间积分项运用一阶卷积求积公式进行离散,并以MacCormack方法的两步预测-校正方法处理非线性项;然后采用四阶紧差分离散空间的一阶和二阶导数,构造了Euler预测-校正紧差分全离散格式。最后通过案例验证了所提出算法的有效性。

基于PINN的Burgers方程求解模型

传统的数值求解方法面临维数灾难和效率与精度平衡问题,而基于数据驱动的神经网络求解方法又存在训练量冗余和不可解释性问题。针对此问题,物理信息神经网络(Physical Information Neural Networks,PINNs)关注了训练数据中隐含的物理先验知识,融合了神经网络拟合复杂变量的能力,赋予了传统神经网络所缺乏的物理可解释性。应用该算法模型,提出了一种基于PINN的Burgers方程求解模型,该算法模型在训练中施加物理信息约束,因此能用少量的训练样本学习预测到分布在时空域上的偏微分方程模型。实验结果表明,在1+1维Burgers方程算例下,所提方法相比于经典的机器学习算法能有效捕抓到方程的变化并进行精确模拟,相比于有限差分法,可以大幅度缩短模拟时间。通过对不同的网络参数进行比较实验,所提方法在10%的噪声破坏下能产生合理的识别准确度,网络逼近方程的待定系数误差在0.001以内。

Bilinear forms through the binary Bell polynomials, N solitons and Backlund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beach

Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N-soliton solutions are worked out, while two auto-B?cklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N-soliton solutions and B?cklund transformations are different from those in the existing literature. All of our results are dependent on the waterwave dispersive power.

Burgers方程的奇摄动初值问题的激波解

利用合成渐近展开法研究具有初值间断的Burgers方程的奇摄动问题.初始条件的突变使得问题的解在过渡层产生激波.首先,在激波位置两侧分别寻求具有边界层性质的近似式;再使用衔接法将对应的曲面光滑地衔接,构成激波解的形式近似;最后,运用渐近展开理论分析解的渐近性质,得到一致有效的渐近展开式.

New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems

On the tangent bundle TSN-1 of the unit sphere SN-l, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel-Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion.

基于Burgers向量提取与分析的改进PRD算法在位错环模拟中的应用

RAFM钢经中子辐照后会产生两种类型的间隙位错环(1/2〈111〉环和〈100〉环),导致长时间服役后出现辐照硬化与脆化现象,因此理清不同类型位错环的形成与转变过程对材料微结构演化及性能预测具有重要意义。本文基于加速分子动力学中的并行副本复制法(PRD),通过分析位错环转变的机理特性,提取Burgers向量,改进了PRD在位错环模拟上的应用,实现了〈100〉环向1/2〈111〉环的加速转变现象模拟。结果表明:在1000 K下,采用改进PRD算法程序进行模拟,小尺寸〈100〉环会发生向1/2〈111〉环的转变,转变时间比传统分子动力学方法更快;大尺寸〈100〉环会出现〈100〉位错段和1/2〈111〉位错段共存的状态,甚至在带有Ni溶质元素的〈100〉环中还发现了完全转变到1/2〈111〉位错环的现象。此外,对程序模拟的准确性进行验证并分析评估了加速性能与并行性能,通过与原PRD算法对比,发现其并行效率远高于原PRD,并行效率在90%左右,且并行规模的增加对于并行性的影响不大,可以很好地进行大规模并行扩展。

考虑沥青混合料空隙率的蠕变特性及改进Burgers模型

为了更为精确的分析不同空隙类型沥青混合料的抗变形性能的影响,在经典的Burgers模型上进行改进,添加了一个非线性元件,得到改进的Burgers模型,将模型的宏观参数转化为离散元PFC的微观参数,植入PFC程序,用于分析不同空隙特征沥青混合料的抗变形性能。结果表明:改进Burgers模型能较好地表征空隙率较大的沥青混合料的蠕变特性,且空隙率较大的沥青混合料在加载过程中相比与空隙率较小的沥青混合料的非线性蠕变变形更为明显,同时,改进Burgers模型可较好地预测在不同温度条件下不同空隙类型的沥青混合料的蠕变变形。用于研究大空隙特征沥青混合料OGFC-13时,当空隙率增大2%时,沥青混合料蠕变变形最大可增大1/2,当空隙率增大10%时,沥青混合料蠕变变形可增大近6倍。