演化方程

显然，扩展的F展开方法也可以解其他类型的非线性演化方程。

Obviously , the extended F-expansion method can be applied to solve other type of nonlinear evolution equations as well .

一类大气演化方程组的Cauchy问题

On the Cauchy Problem of One Type of Atmosphere Evolution Equations

（1+1）维非线性演化方程的B样条Galerkin有限元数值解

B-Spline Galerkin Finite Element Numerical Solutions for ( 1 + 1 ) - Dimensional Nonlinear Evolution Equation

Tu族演化方程的换位表示

Commutator Representations for the Tu Hierarchy of Evolution Equations

通过对协同学基本演化方程的变换，运用logistic方程描述了冶金企业技术创新四种方式的协同机理。

Through transferring the basic synergetic evolvement equation , the logistic equations are used to describe the coordination mechanism of four innovative modes .

Lam函数和非线性演化方程的多级准确解的不变性

Lam è function and invariants of multi-order exact solutions among nonlinear evolution equations

双波理论被应用于描述任意维q变形振子，得到了各维力学量随时间演化方程。

Double wave description of the motion of arbitrary - dimensional q - deformed oscillator is obtained . The time evolution equations of related physical quantities are derived .

用齐次平衡原则和辅助微分方程方法得到了6个重要的n次非线性演化方程的孤立波解。

The solitary wave solutions for six important nonlinear evolution equations with n degree nonlinearity are obtained by the homogeneous balance principle and sub-ODE method ( mean by subsidiary ordinary differential equation method ) .

演化方程的Darboux变换的一类求法

A Method of Searching Darboux Transformations for the Evolution Equations

利用双波理论描述三维各向异性q变形振子各力学量随时间的演化方程，结果显示粒子做非线性振动。

Time - dependent physics equation of three - dimensional q - deformed oscillator are describes with Double - Wave . All results show the movement of particle is nonlinear .

一类新的圈代数和它的Liouville可积演化方程族

One class of new loop algebra and its Liouville integrable hierarchy of evolution equations

建立了BoomClay横观各向同性弹塑性损伤本构模型并给出了损伤演化方程，该模型可以考虑泥岩的强化和软化行为。

Transversely isotropic elasto-plastic damage constitutive model and the damage evolution equation are established considering modified Mohr-Coulomb criterion . The model can describe the hardening and softening behavior of Boom Clay .

在小x区域，当考虑到重组效应时，线性演化方程已经不能完全描述部分子之间的相互作用，必须引入非线性项对其进行修正。

When considering the recombination phenomenon in small x region , linear evolution equation can not be used to describe the interactions of partons , and a nonlinear term must be added to amend the evolution equation .

基于这种调制稳定性，给出了由光生伏打自散焦非线性支持的一维灰空间孤子的演化方程，并在光生伏打光折变LiNbO3∶Fe晶体中给出了它的静态解。

Based on such modulation stability , the evolution equations for one-dimensional gray spatial solitons supported by the photovoltaic self-defocusing nonlinearity are presented and its stationary solution in photovoltaic photorefractive crystal LiNbO_3 ∶ Fe is given .

基于CT试验结果，对岩石应力－应变全过程曲线进行了分段，从工程应用出发，给出了峰前分段岩石损伤演化方程及本构关系。

Based on the CT testing results , the complete rock stress-strain process curve is divided into several . From the point of view of engineering application , the pre-peak 3-segment damage evolution equation and constitutive model of rock are given .

马氏体体积分数的演化方程为一个关于每个取向变体在该晶粒内所占体积分数fR的演化率为变量的积分方程。

The evolution of martensitic volume fraction can be expressed by an integral equation , whose variable is the rate at which the volume fraction the ratio of the volume of each variant to that of corresponding grain varies .

主要从CT技术的检测原理、岩石损伤的直接检测、三轴或单轴条件下岩石的破坏机理及演化方程和本构关系等方面概述了岩石细观损伤特性试验研究现状及进展。

The state-of-art and development in meso-damage of rock experiment is introduced by checking the measuring principle of CT , doing direct measuing of rock damage , and studying damage mechanism of rock in triaxial or uniaxial conditions , evolution equations and constitutive relations .

本文用Snake的内部能量作为图像水平线的先验模型，由它的梯度下降流得到关于图像曲面的演化方程。

The internal energy of the Snake is used as the prior model of the level lines of the image , and from its descent flow we obtain the evolution equation of the image surface .

基于Curren以及白以龙等通过回收实验获得的经验规律，并借鉴封-经模型建立了损伤演化方程。

Based on the results of recovered experiments the law of damage evolution is phenomenally established .

借助Maple软件，采用吴方法及改进的齐次平衡法，研究了一类非线性演化方程的精确行波解。

With the help of software Maple , Wu 's method and Improved Homogeneous Balance Method are used to study exact traveling solutions of a kind of nonlinear evolution equation .

因此，文献[15，16]分析了对AP方程的高扭度修正过程，利用时序微扰论（TOPT）导出了新的考虑高扭度修正的演化方程，简称MAP方程。

So the works [ 15,16 ] set up a new evolution equation called MAP equation by time ordered perturbative theory ( TOPT ) which considers the higher twist processes .

推广了Jacobi椭圆函数展开方法，研究了复非线性演化方程组的求解问题，得到了长短波相互作用方程的准确包络周期解。

In this paper , the Jacobi elliptic function method is generalized to study nonlinear evolution system . The envelope periodic solutions of long-short wave interaction equation are obtained .

应用双波函数理论，得到了一维Morse势中粒子运动状态的力学量的时间演化方程。

The double-wave function quantum theory is applied to gain the time evolution equation to describe the physical quantities of a single motional particle in the one-dimensional Morse potential .

在此动力学区域部分子的密度很大，根据高扭度修正过的AP演化方程（MDAP方程），分析了此区域的部分子饱和问题。

With the high twist modified AP evolution equation ( MDAP equation ), the saturation problem of partons at LHC energies is analyzed .

运用自组织理论和方法建立河湾的演化方程.结合Fokker-Planck方程解析解的性质与Langevin方程的动力学特征，推断河湾演变的基本规律如对称破缺、形态转变、演变趋势及速度等。

The evolution equations of river bends are proposed by using the self-organized theory and method which are the Fokker-Planck equation and the Langevin equation .

通过选取恰当修正项，由零曲率方程获得一族新的Lax可积系，作为其约化情形，得到了一类耦合非线性演化方程。

By choosing proper modified terms , a new Lax integrable system is presented via the use of zero-curvature equation . As its reduction , a coupled nonlinear evolution equation is followed .

根据原状膨胀土在非饱和三轴剪切试验过程中的CT扫描结果，定义了一个基于CT数据的原状膨胀土的结构损伤变量，建立了剪切过程中膨胀土的损伤演化方程。

Based on the computerized tomography ( CT ) scanning results of natural expansive soil during triaxial shearing test , a damage variable of natural expansive soil is derived from the computerized tomography scanning data , and the damage evolution equation of expansive soil during shearing is also developed .

利用声发射累积相对能量定义损伤变量，通过单纤维束模型、平均杆元模型以及体积平均化模型初步建立了纤维束、二维编织、三维编织C／SiC复合材料拉伸损伤演化方程。

Damage evolution equations in the tensile process were formulated , using AE accumulative relative energy as a damage variable , based on single bundle model , average rod model and volume-averaged model , for single bundle , 2-D woven and 3-D braided C / SiC composites respectively .

结合HERA有关核子结构函数与其斜率的实验数据，讨论了在量子色动力学演化方程中存在高扭度重组效应的可能性。

With the HERA experiment data of nucleon structure function and it 's slope , we discuss the probability of higher twist recombination effect in Quantum Chromodynamics evolution equation .

利用双波函数理论描述三维各向同性q变形振子力学量随时间的演化方程，结果显示粒子做非线性振动.同时，当r→0时，所有结论退化为普通三维各向同性谐振子的相关结果

Time-dependent equation of three dimensional isotropic q deformed oscillators are describes with double wave interpretation physics equation , the results show that movement of particle is nonlinear At the same time , when r → 0 , the theory reduces to the common three dimensional isotropic oscillator theory