Exact Analytic N-Soliton-Like Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics

在液体动力学和血浆适用，一个概括 variable-coefficientKorteweg-de Vries (vcKdV ) 模型被调查。为如此的一个模型的双线性的形式和分析 N-soliton-likesolution 被 Hirota 方法和 Wronskian 技术导出。另外，双线性的 auto-Backlund 转变在之间(N-1 )-soliton-like 和 N-soliton-like 答案 isverified。

Existence of Formal Conservation Laws of a Variable-Coefficient Korteweg-de Vries Equation from Fluid Dynamics and Plasma Physics via Symbolic Computation

采用能被用来为标准 Korteweg-de Vries (KdV ) 方程表明无限的能量守恒定律的方法，我们证明在 Painleve 测试条件下面的可变系数的 KdV 方程也拥有正式能量守恒定律。

Darboux Transformation and Soliton Solutions for a Variable-Coefficient Modified Kortweg-de Vries Model from Fluid Mechanics, Ocean Dynamics, and Plasma Mechanics

这份报纸是调查可变系数的修改 Kortweg-de Vries (vc-mKdV ) 为力学建模，它从液体力学，海洋动力学，和血浆描述一些状况。由 AblowitzKaupNewellSegur 过程和符号的计算， vc-MKdV 模型的宽松的对被导出。基于上述的宽松的对，然后， Darboux 转变被构造，一个新 one-soliton-like 答案也被获得。one-soliton-like 答案的特征被分析并且图形地讨论了在 solitonlike 繁殖说明可变系数的影响。

Various Methods for Constructing Auto-Bcklund Transformations for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics

<Abstract>In this paper,under the Painlevé-integrable condition,the auto-Bcklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method,truncated Painlevé expansion method,extended variable-coefficient balancing-act method,and Lax pair.Additionally,the compatibility for the truncated Painlevé expansion method and extended variable-coefficient balancing-act method is testified.

Infinite Sequence of Conservation Laws and Analytic Solutions for a Generalized Variable-Coefficient Fifth-Order Korteweg-de Vries Equation in Fluids

在这份报纸，为在液体的一个概括可变系数的第五顺序的 Korteweg-de Vries 方程的能量守恒定律的一个无限的序列基于 B 被构造 ? cklund 转变。Hirota 双线性的形式和符号的计算被使用获得三种答案。可变系数能影响典型的线的保存密度，联系流动，和外观。soliton 结构上的波浪数字的效果也被讨论并且 soliton 结构打字，例如，双 periodic soliton，平行 soliton 和 soliton 建筑群，被介绍。

Painlevé Analysis,Soliton Solutions and Bcklund Transformation for Extended (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations in Fluid Mechanics via Symbolic Computation

This paper is to investigate the extended(2+1)-dimensional Konopelchenko-Dubrovsky equations,which can be applied to describing certain phenomena in the stratified shear flow,the internal and shallow-water waves, plasmas and other fields.Painleve analysis is passed through via symbolic computation.Bilinear-form equations are constructed and soliton solutions are derived.Soliton solutions and interactions are illustrated.Bilinear-form Backlund transformation and a type of solutions are obtained.

Effect of void size and Mg contents on plastic deformation behaviors of Al-Mg alloy with pre-existing void:Molecular dynamics study

The plastic deformation properties of cylindrical pre-void aluminum-magnesium(Al-Mg)alloy under uniaxial tension are explored using molecular dynamics simulations with embedded atom method(EAM)potential.The factors of Mg content,void size,and temperature are considered.The results show that the void fraction decreases with increasing Mg in the plastic deformation,and it is almost independent of Mg content when Mg is beyond 5%.Both Mg contents and stacking faults around the void affect the void growth.These phenomena are explained by the dislocation density of the sample and stacking faults distribution around the void.The variation trends of yield stress caused by void size are in good agreement with the Lubarda model.Moreover,temperature effects are explored,the yield stress and Young’s modulus obviously decrease with temperature.Our results may enrich and facilitate the understanding of the plastic mechanism of Al-Mg with defects or other alloys.

Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation

A gas-kinetic numerical method for directlysolving the mesoscopic velocity distribution functionequation is presented and applied to the study ofthree-dimensional complex flows and micro-channelflows covering various flow regimes.The unified velo-city distribution function equation describing gas trans-port phenomena from rarefied transition to continuumflow regimes can be presented on the basis of the kineticBoltzmann-Shakhov model equation.The gas-kineticfinite-difference schemes for the velocity distributionfunction are constructed by developing a discrete velo-city ordinate method of gas kinetic theory and an uns-teady time-splitting technique from computational fluiddynamics.Gas-kinetic boundary conditions and nume-rical modeling can be established by directly manipu-lating on the mesoscopic velocity distribution function.A new Gauss-type discrete velocity numerical integra-tion method can be developed and adopted to attackcomplex flows with different Mach numbers.HPF paral-lel strategy suitable for the gas-kinetic numerical methodis investigated and adopted to solve three-dimensionalcomplex problems.High Mach number flows aroundthree-dimensional bodies are computed preliminarily with massive scale parallel.It is noteworthy and ofpractical importance that the HPF parallel algorithmfor solving three-dimensional complex problems canbe effectively developed to cover various flow regimes.On the other hand,the gas-kinetic numerical methodis extended and used to study micro-channel gas flowsincluding the classical Couette flow,the Poiseuille-channel flow and pressure-driven gas flows in two-dimensional short micro-channels.The numericalexperience shows that the gas-kinetic algorithm may bea powerful tool in the numerical simulation of micro-scale gas flows occuring in the Micro-Electro-MechanicalSystem (MEMS).

Darboux Transformation and Explicit Solutions for Discretized Modified Korteweg-de Vries Lattice Equation

修改 Korteweg-de Vries (mKdV ) 打了方程能被用来在液体，血浆，和光学描述某些非线性的现象。在这份报纸， discretized mKdV 格子方程被调查。在符号的计算的帮助下，分离矩阵光谱为那个系统的问题被构造。为那个系统的 Darboux 转变基于结果被建立光谱问题。明确的答案经由 Darboux 转变被导出。那些解决方案的结构图形地被显示出，它可能是有用的在液体，血浆，和光学理解一些物理进程。

Wronskian and Grammian Determinant Solutions for a Variable-Coefficient Kadomtsev-Petviashvili Equation

在这篇论文，我们为一个可变系数的 Kadomtsev 打 Petviashvili 的方程导出双线性的形式。基于双线性的形式，我们获得 Wronskian 决定因素答案，它确实被证明是通过 Wronskian 技术的这个方程的一个准确答案。另外，我们证明那这个方程能被借助于 Pfaffian 衍生物公式把它的答案看作一个 Grammian 决定因素归结为 Jacobi 身份。

Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations

Kortweg-de Vries (KdV ) 打了方程被用来在液体和血浆描述某些非线性的现象。概括复杂联合 KdV (GCCKdV ) 方程在这份报纸被调查。通过依赖可变转变和符号的计算， GCCKdV 方程被转变成他们的双线性的形式， one-soliton 和 two-soliton 解决方案基于被获得。通过二 solitons 的相互作用，常规有弹性的碰撞被显示出。当波浪数字是复杂的时，三种 solitonic 碰撞被介绍：(i) 二 solitons 合并并且周期性地与对方分开；(ii ) 吸引力和排斥将近两次，并且最后在相互作用的如此的类型以后与对方分开的二 solitons 展览；(iii ) 二 solitons 在碰撞的中央区域是变动的。solitons 的繁殖特征在考虑的 GCCKdV 方程与系数的效果被调查。有增加的 soliton 增加的速度。有与增加增加和减少的 v 增加的振幅。

Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation

在这篇论文，我们把我们的焦点放在一个可变系数的第五顺序的 Korteweg-de Vries (fKdV ) 方程上，它拥有很多优秀性质并且具有物理、工程的领域里的当前的重要性。某些限制被得出，它确认如此的一个方程的 integrability。在那些限制下面，一些 integrable 性质被导出，例如宽松的对和 Darboux 转变。经由 Darboux 转变，它是以一种递归的方式产生解决方案的一个可实行的方法， one-solitonic 和 two-solitonic 解决方案被介绍，一些域里的这些 solitonic 结构的相关物理应用程序也被指出。

Gas-kinetic numerical schemes for one- and two-dimensional inner flows

Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated and analyzed based on the computed results. The ways of improving the computational efficiency of the gas-kinetic numerical method and the computing principles of difference discretization are discussed.

N-Fold Darboux Transformation and Bidirectional Solitons for Whitham-Broer-Kaup Model in Shallow Water

Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kaup system whose Lax pair can be derived by the Ablowitz-Kaup-Newell-Segur technology. With symbolic computation, based on the aforementioned Lax pair, the N-fold Darboux transformation is constructed with a gauge transformation and the multi-soliton solutions are obtained. Finally, the elastic interactions of the two-soliton solutions (including the head-on and overtaking collisions) for the WBK system are graphically studied. Those multi-soliton collisions can beused to illustrate the bidirectional propagation of the waves in shallow water.

Low-diffusion preconditioning scheme for numerical simulation of low-speed flows past airfoil

The preconditioning technique can address the stiffness of a low Mach number flow,while its stability is poor.Based on the conventional preconditioning method of Roe’s scheme,a low-diffusion scheme is proposed.An adjustable parameter is introduced to control numerical dissipation,especially over the dissipation in the boundary layer and extremely in a low speed region.Numerical simulations of the low Mach number and low Reynolds number flows past a cylinder and the low Mach number and high Reynolds number flows past NACA0012 and S809 airfoils are performed to validate the new scheme. Results of the three tests well agree with experimental data,showing the applicability of the proposed scheme to low Mach number flow simulations.

Painlevé analysis, auto-Bäcklund transformations, bilinear forms and soliton solutions for a(2+1)-dimensional variable-coefficient modified dispersive water-wave system in fluid mechanics

In this paper,we investigate a(2+1)-dimensional variable-coefficient modified dispersive waterwave system in fluid mechanics.We prove the Painlevéintegrability for that system via the Painlevéanalysis.We find some auto-B?cklund transformations for that system via the truncated Painlevéexpansions.Bilinear forms and N-soliton solutions are constructed,where N is a positive integer.We discuss the inelastic interactions,elastic interactions and soliton resonances for the two solitons.We also graphically demonstrate that the velocities of the solitons are affected by the variable coefficient of that system.

Solitons and periodic waves for a generalized(3+1)-dimensional Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

Under investigation in this paper is a generalized(3+1)-dimensional Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics.Soliton and one-periodic-wave solutions are obtained via the Hirota bilinear method and Hirota-Riemann method.Magnitude and velocity of the one soliton are derived.Graphs are presented to discuss the solitons and one-periodic waves:the coefficients in the equation can determine the velocity components of the one soliton,but cannot alter the soliton magnitude;the interaction between the two solitons is elastic;the coefficients in the equation can influence the periods and velocities of the periodic waves.Relation between the one-soliton solution and one-periodic wave solution is investigated.

Bell-Polynomial Approach and Soliton Solutions for Some Higher-Order Korteweg-de Vries Equations in Fluid Mechanics,Plasma Physics and Lattice Dynamics

The Korteweg-de Vries(Kd V)-type equations have been seen in fluid mechanics,plasma physics and lattice dynamics,etc. This paper will address the bilinearization problem for some higher-order Kd V equations. Based on the relationship between the bilinear method and Bell-polynomial scheme,with introducing an auxiliary independent variable,we will present the general bilinear forms. By virtue of the symbolic computation,one-and two-soliton solutions are derived.

局部扩大段参数对高速列车过隧道引起的压力波动的影响规律（英文）

数值模拟研究了局部扩大段参数对高速列车过隧道引起的压力波动的影响规律。对比验证了光滑壁面隧道的实验数据和由结构及非结构网格计算获得的数值模拟结果。对三个局部扩大段参数进行了数值模拟研究:局部扩大段沿隧道周向分布、局部扩大段截面积和局部扩大段沿隧道长度方向分布。数值模拟结果表明:局部扩大段沿各隧道周向位置分布的压力波动基本相同。存在一个最佳的局部扩大段截面积使得压力变化幅值和平均压力差值为最小值。获得了压力变化幅值和平均压力差值随局部扩大段沿隧道长度方向分布的变化规律。