李群变换求解一维非线性有限变形固结问题(英文)

在对渗透系数与孔隙比以及有效应力与孔隙比的关系作出假设的基础上 ,讨论了不同初值和边值条件下的饱和粘土一维非线性有限变形固结方程 ,同时对不同边界条件的性质进行了评价。研究表明 ,对于一些相对简单的边界条件 ,通过李群变换的方法可以得到非线性固结方程的完整解析解。最后 ,将所得到的解答与Tan&Scott的有关解答进行了分析比较 。

一维大应变固结理论的对称性及Lie群变换求解

运用Lie群变换方法探讨了一维大应变非线性固结方程的对称性,详细分析在该对称性的意义下求解不同条件下这类非线性偏微分方程解析解答的可能性,分别给出了各类情况下的偏微分方程系数的相应表达式.

半无限体地基一维非线性大变形固结解析分析方法研究

基于有效应力与孔隙比以及渗透参数与孔隙比之间的关系的一些假定 ,采用李群变换求解考虑材料非线性和几何非线性的半无限均质土体大变形固结非线性偏微分方程 ,得到了一个不考虑自重固结的完全解析解。将其计算结果与传统固结理论作分析比较 ,发现两者的差别与土性非线性指标有关。计算结果还表明 。

饱和土体自重固结问题的相似解

采用了比以往更为普遍的土体物理力学性质假设,利用Hopf_Cole变换方法求得了厚层土体在自重应力作用下的非线性固结问题的完整解析解答.通过试验数据,将该解答与传统的大应变线性固结理论解答和基于实验数据的有限元数值解答相比较,结果表明,该解答能够更好地描述土体的实际固结过程,而由线性化固结理论所得的解答对固结过程中的沉降量和固结度的估计偏小.

一维大应变固结理论的一类解析解

简述了一维固结理论的发展 ,研究了不同描述方法下固结系数的定义 ,运用变换群的方法求得了某些条件下一维大应变固结方程的完整解析解答 ,在此基础上与相同条件下的小应变固结理论作了比较 ,并通过对实例的计算 ,分析了不同假设条件下一维固结理论之间的差异 .计算结果表明 ,在固结过程中 ,由大应变固结理论所得出的沉降量要大于由小应变理论所得出的沉降量 ,而两种固结理论所得出的最终沉降量相同 .

变系数x—kdv广义kdv方程的相似分析和精确解

本文采用标准的相似变换求得了变系数x—kdv、广义kdv方程的一族精确解。在一定的条件下说明了这些方程的可积性。最后讨论了对应这些精确解的无穷小变换群。

On New Invariant Solutions of Generalized Fokker-Planck Equation

The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported.

Symmetry Analysis of Nonlinear Incompressible Non-Hydrostatic Boussinesq Equations

The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.

Finite Symmetry Transformation Groups and Exact Solutions of Konopelchenko-Dubrovsky Equation

Based on the general direct method developed by Lou et al. [J. Phys. A： Math. Gen. 38 （2005） L129], the symmetry group theorem is obtained, from that both the Lie point groups and the non-Lie symmetry groups of the Konopelchenk-Dubrovsky （KD） equation are obtained. From the theorem, some exact solutions of KD equation are derived from a simple travelling wave solution and a multi-soliton solution.

Herz Spaces on Nilpotent Lie Groups and Its Applications

In this paper, we define Herz type spaces on nilpotent Lie groups and give the boundedess of heat kernel and Riesz transform on Herz spaces.

Lie Reduction and Conditional Symmetries of Some Variable Coefficient Nonlinear Wave Equations

Lie symmetry reduction of some truly ＂variable coefficient＂ wave equations which are singled out from a class of （1 ＋ 1）-dimensional variable coefficient nonlinear wave equations with respect to one and two-dimensional algebras is carried out. Some classes of exact solutions of the investigated equations are found by means of both the reductions and some modern techniques such as additional equivalent transformations and hidden symmetries and so on. Conditional symmetries are also discussed.

拓扑流及其应用专题·编者按

物理学的主要任务之一是探索微观世界的基本规律，而这些规律主要表现为在某种变换下的不变性、时空变换下的不变性——能量动量守恒、以及电子场在李群的变换下导致电荷守恒和电磁场的自然存在等等．而且自然界中还存在一种比李群变换更一般的变换——拓扑变换，拓扑变换下的不变性也对应某种守恒律或守恒量．物理学家在量子场论的研究中发现了磁单极、涡旋解和Skyrmion，后两者己在凝聚态中被发现．其中，Skyrmion是20世纪60年代物理学家在研究核子时引入的，核子的重子数是1，而Skyrmion流的荷数也是1．这些解具有拓扑性质．

REPRESENTATIONS OF SOLVABLE LIE GROUPSAND GEOMETRIC QUANTIZATION

Representations of solvable Lie groups are realized and classified by geometric quantization of coadjoint orbits through positive polarizations.