查询词典 soliton

The interactions between two semifolded solitons are elastic,while the interactions among other nonlinear multivalued and single valued excitation patterns such as the interactions between semifolded soliton and single valued localized soliton,semifolded soliton and folded soliton,and the interaction among semifolded soltion,folded soliton and single valued localized solitons,are nonelastic generally,which reveal different exotic and important nonlinear mechanical properties.

半折叠孤子之间的非线性相互作用是弹性，而半折叠孤子与单值局域孤子、半折叠孤子与折叠孤子以及更复杂的半折叠孤子、折叠孤子、单值局域相干孤子之间等多值和单值非线性激发模式间的相互作用是非弹性的，呈现出多样的非线性特性。

The results show that the change of modulation period and modulation depth affect the period of soliton interaction and the difference of relative amplitude barely affects period of soliton interaction. In particular the lattice soliton interaction is effectively avoided by opposite phase soliton.

结果表明：调制周期和调制深度的变化影响了格子孤子相互作用的周期大小，而相对振幅的差异对孤子相互作用的周期影响较小，特别是反相孤子能够有效控制格子孤子的相互作用。

Selecting proper single valued variable separation functions in the 2+1 variable separation solutions,we construct many types of single valued coherent soliton structures such as dromion,dromion lattice,solitoff,2-solitoff,static and kinetic breather,instanton,compacton, peakon,and so on.The interactions among these coherent localized excitations including the collisions of compaction and compacton,peakon and peakon,line soliton and y-periodic soliton,dromion and dromion,dromion and solitoff,et al,are investigated analytically and graphically,and found that can be elastic and nonelastic respectively,which reveal various exotic and important nonlinear characters and interaction properties.

在2+1维分离变量解中选择适当的的单值分离变量函数，构造了2+1维非线性波动模型多种单值相干孤子结构如Dromion，Dromion格子，Solitoff，2-Solitoff，静止和运动呼吸子、瞬子、Compacton、Peakon等；考察了一些典型的非线性激发模式间如Compacton和Compacton，Peakon和Peakon，线孤子和y-周期孤子，Dromion和Dromion，Dromion和Solitoff之间等相互作用行为，发现其相互作用可以弹性的也可以是非弹性的，揭示了多样奇异而重要的非线性特性。

With the bell-type soliton movement in supersonic speed and the kink-type soliton movement in subsonic speed the two types of the soliton bound states appear to situate at the bottom and the top of the exciton energy band respectively.

对Bell一型孤子以亚声速＜运动，而Kink一型孤子以超声速运动，它们分别出现在激子能带底部和顶部。

In relativistic non-linear field theory,topological defects are a kind of topological soliton.Soliton star is a soliton with star mass and star size.

孤子星是相对论性非线性场论中的拓扑缺陷，这类拓扑缺陷具有恒星到星系的质量。

By means of the undetermined coefficient method ,which is submitted in reference for solving nonlinear wave equations for their peaked soliton solutions ,three kinds of peaked soliton solutions are obtained for two important nonlinear wave equations— Korteweg-de Vries equation and Benjamin-Bona-Mahonyequation,respectively. One kind of peaked compacton solution ,which has the characteristics of both peaked soliton solution and compacton solution ,is obtained for above two equations with the aid of transformation relation between triangle function and hyperbolic function,. By use of above solutions, two kinds of periodic peaked traveling wave solutions are constructed.

摘 要：利用文献中提出的求非线性波方程尖峰孤子解的方法，分别求解了两个重要的非线性波方程—Korteweg-de Vries 方程和Benjamin-Bona-Mahony BBM）方程，得到了3类尖峰孤子解；借助双曲函数与三角函数间的变换关系得到了1类尖峰紧孤子解，该型解兼有尖峰孤子解和紧孤子解的特点；在上述结果的基础上构造了2个周期性的尖峰行波解。

According to the characteristics of peaked soliton solution, the undetermined coefficient method for solving nonlinear wave equations for their peaked soliton solutions is submitted and by means of the method several kinds of peaked soliton solutions are obtained for five nonlinear wave equations: the Camassa-Holm, fifth -order KdV-like, generalized Ostrovsky, combined KdV-mKdV and Klein-Gordon equations.

刘煜 河南电力试验研究院，郑州 450052根据尖峰孤子解的特点，提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法，并利用该方法求解了5个非线性波方程，即CH（Camassa-Holm方程、五阶KdV-like 方程、广义Ostrovsky方程、组合KdV-mKdV方程和Klein-Gordon方程，比较简便地得到了这些方程的尖峰孤子解。

Although the Preissman scheme of KP equation is multisymplectic, it took too efforts to realize, Hence we elimate the auxiliary variable by a trivial computation and obtained the multisymplectic forty-five points scheme of KP equation. And then, we test this forty-five points scheme on soliton and solitary waves over long time intervals, the numerical results shows the propagation and interact of soliton and solitary waves.

但是在实际的数值实验中，由于需要计算共轭动量的值，Preissman格式需要占用的计算内存比较大，计算时间比较长，因此我们在数值格式中消去共轭动量，最后得到与多辛Preissman格式等价的一个多辛45点格式，我们用这个格式进行了数值实验，数值实验结果很好地显示了孤立子和孤立波的传播与碰撞。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

The thesis analyzes the quantum properties of the soliton combining the analytic and numerical method. It includes the following several parts (the bold parts are creative work): 1. We obtained the quantum field equation of optical soliton in the lossy fiber by means of heat reservoir theory.

本论文采用解析与数值模拟相结合的方法来分析孤子的量子特性，主要内容包括以下几个方面（黑体部分属于创新性的工作）： 1、用热库理论得到了考虑光纤损耗的光孤子传输的量子场方程。

Vishnu entered a dark fourth dimensional dream that did not support his field or continued life.

毗瑟挐进入了一个第四密度的黑暗梦想，那里并不支持他的能量场或继续生命。

Leaders and decision-making persons use it to collect the data, including the information of unit work, handing in fee, oweing fee, prepaying fee,changing and afterpaying and account transfering of joining-insurance employee, and account paying of all kinds of insurances from hospitalization insurance institutions.The collected data is picked up, organized, switched and showed to user.

该子系统主要面向各级领导、决策分析人员；从各个医疗保险经办机构和定点医疗机构采集数据，包括在各个医疗保险经办机构处理的单位办公信息，单位缴费、欠费、预缴费信息，参保职工变更信息，参保职工增减变动信息，参保职工补缴信息，参保职工帐户划拨信息：包括各定点医疗机构处理的各险种帐户支出信息，各险种的统筹金支付信息等；将采集的数据提取，组织和转换，然后展示给用户。