查询词典 evolution equation

By using the solutions of a new auxiliary elliptic equation,a direct algebraic method is proposed to construct the exact solutions of some nonlinear evolution equations.The main difference between this method and previous auxiliary elliptic equation methods is that the balance order becomes smaller after using the new auxiliary elliptic equation.Therefore,the derived algebraic equations are greatly simplified.

利用一个新的辅助椭圆方程将求解非线性发展方程精确解的问题转化为一个代数方程组进行求解，与已有的辅助椭圆方程法的主要不同是，应用这一新的辅助椭圆方程后降低了平衡次数，减少了所得的代数方程组的个数和方程的项数，从而大大地简化了代数方程组的求解。

It is hardly to get and express the solution of the equation of evolution by the analysis, so it used to solve the equation by numerical method.

根据解析的方法求发展方程的解，并且通过已知函数表示出来。

Waxman-Smits equation is an evolution of Acrhie equation for shaly sands, and it is a nonlinear equation.

Waxman-Smits方程是阿尔奇方程在泥质砂岩地层中的推广，W-S方程为非线性方程。

The time evolution of a quantum state is described by the Schrodinger equation, in which the Hamiltonian, the operator corresponding to the total energy of the system, generates time evolution.

薛定谔方程描述量子态的时间演化，在量子态哈密尔敦函数中，操作者与系统的总能量通讯，引起时间演化。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

In the model, the evolution equation of damage was introduced and the time-dependent effect and nonproportional path effect was taken into account.

该模型中引入了损伤演化方程，考虑了时相关效应和非比例效应，并将损伤分为时无关损伤和时相关损伤两部分，并采用不同的损伤演化方程来描述这两类损伤。

Based on the statistical damage evolution equation considering stress damage threshold and the multiple rheological model of gypsum breccias, the damage rheological constitutional model is established from hypothesis of strain equivalence. The calculated results of the model agree well with creep test results.

在Kachanov提出的一维蠕变损伤演化方程的基础上，建立了同时考虑瞬时损伤和蠕变损伤的流变本构模型，理论值与试验值基本一致，验证了提出的蠕变损伤演化方程是正确的，所建的损伤流变模型能够较好地描述石膏角砾岩的加速蠕变阶段。

The good agreement of theoretical data with test data shows that the creep damage evolution equation put forward is rational and the damage rheological constitutional model established can describe the accelerated creep stage of gypsum breccias well.

提出了&分段外推&的思想来提高神经网络模型对时间的外推性，同时，为了增加每段外推的稳定性，提出了&初次训练&的方法；以考题为例，验证了所提方法的优越性。

Specially, we use multi-point crossover to obtain schemata evolution equation instead of one-point crossover.

引 言进化算法是借用生物进化的思想，在现代遗传学的启发下，发展起来的一种启发式的随机搜索优化方法。

Based on Betti energy iterative law, the damage deformation mechanism of fractured rock mass under stress and seepage pressure has been studied. Furthermore 3D elastic and elastoplastic damage-fracture constitutive relation and damage evolution equation considering seepage pressure have been established.

基于Betti能量互易定理，系统研究了应力场与渗流场共同作用下的岩体损伤演化机制，建立了考虑渗透压力的三维含水裂隙岩体脆弹性和弹塑性断裂损伤本构模型和损伤演化方程。

What are your goals and strategies for growth?

你的成长目标和策略是什么？

And unto the angel of the church in Sardis write; These things saith he that hath the seven irits of God, and the seven star I know thy works, that thou hast a name that thou livest, and art dead.

3：1 你要写信给撒狄教会的使者，说，那有神的七灵和七星的，说，我知道你的行为，按名你是活的，其实是死的。