integrable system

Symmetry Constraint and a New Completely Integrable System

对称约束与一个新的完全可积系统

In chapter one , we give a brief introduction to the Hamiltonian method of integrable system .

本文第一章介绍可积系统的哈密顿方法。

A New Integrable System and Its Bi - Hamiltonian Structure

一族新的可积系及其双哈密顿结构

A new infinite dimensional Liouville integrable system and its transformation

一个新的无限维Liouville可积系及其变换

On completely integrable system of linear PDEs with involutive characteristic set method

确定线性偏微分方程组可积系统的对合特征集方法

In chapter 2 , we introduce a " integrable system " and make a research on its general nature .

第二章提出了可积系统概念，研究了该系统的一般性质。

Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System

二维可积系统的求迹公式和周期轨道的量子化

A Mechanical Algorithm for Proving the Completeness of the Solutions of the Formal Integrable System

验证形式可积系统解的完备性的机械化算法

Infinite Number of Integrals of Motion in Classically Integrable System With Boundary (ⅱ)

边界不相关可积系统中无穷多运动积分的研究（Ⅱ）

Bifurcation of Cubic Integrable System under Cubic Perturbation ; three-dimensional dynamic spectrum analyser

一类三次可积系统在三次扰动下的分支三维动态频谱分析仪

Li-chen 's eigenvalue problem and an associated classical integrable system

李-陈方程族及与其相联系的经典可积系统

A Completely Integrable System in the Liouville Sense

一个Liouville完全可积系统

Bifurcation of a Quadratic Integrable System under Quadratic Conservative Perturbations

一个二次可积系统在二次保守扰动下的分支

The Integrable System Associated with Higher-order Constraint

和高阶约束相联系的可积系统

Basing on the Reid and others standard form concept of the formal integrable system is led in .

在Reid等人标准型概念的基础上，引进形式可积系统的概念。

A New Lax Integrable System and Its Liouville Integrability

一族新的Lax可积系及其Liouville可积性

The question on bifurcation of limit cycles in quadratic conservative perturbations of a quadratic integrable system is discussed .

研究了一个具有同宿轨的二次可积系统在二次保守扰动下的分支现象。

Firstly , we give a basic notion and basic theory of C-D pair and C-D integrable system and then we study their applications .

首先给出了C-D对和C-D可积系统的基本理论，然后是具体研究了它们的应用。

A Finite-dimensional Integrable System

一个有限维可积系统

It is studied that the CMC surfaces in the sphere space of dimension 3 by means of integrable system and its spectral transformation is given .

利用可积系统的方法研究3维球空间中的常中曲率（CMC）曲面，并给出了曲面的谱变换。

Part I ( chapter I ) is a brief introduction of the background for integrable system and newest developments about the CM and RS models .

在第一部分（第一章）我们给出本文中要用到的关于可积系统的一般背景以及关于CM模型和RS模型研究的最新进展。

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 .

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。

Two topics of the dissertation research about the integrable system of the soliton equations include : the formulation and integrability of the nonlinear evolution hierarchy as well as their expanding integrable systems .

本文主要从两个方面研究了孤立子方程的可积系统：即非线性演化方程族的生成及可积性质和非线性演化方程族的扩展可积模型。

In this paper , we prove that the real quadratic system with one real straight line solution and two conjugate complex straight lin solutions is integrable system , so it do not has any limit cycle .

本文证明了具有一条实积分直线和一对共轭复积分直线的实二次系统都是可积系统，因而不可能存在极限环。

In fact the discrete integrable system can be used as the model of some problem in physics , chemistry and biology , for example the Toda lattice equation and the Volterra lattice equation .

众所周知，在物理学、化学及生物学中的许多些现象是以微分&差分方程作为模型建立起来的，如Toda晶格方程和Volterra晶格方程等。

And a mechanical algorithm for proving the completeness of the solutions of the formal integrable system is given . By using this method , the problem about the completeness of the Hu 's solutions in elasticity is proven .

并给出验证形式可积系统解的完备性的机械化算法，并用此方法证明了各向同性弹性力学方程组的胡海昌解的完备性问题。

It is has been known that the energy spectra statistic of a chaotic system agrees with Wigner distribution which is achieved from Random Matrix Theory and the one of a integrable system is Poisson distribution achieved originally from the irregular spectra .

一个经典混沌系统的量子能谱统计分布满足由随机矩阵理论所导出的Winger分布，而可积系统满足无规能谱的统计分布即泊松分布。

A multi-component KP hierarchy from the 2 × 2 Sato matrix theory is deduced and discussed . A new Darboux transformation for this hierarchy , the 1 + 1 dimensional integrable system constrained from these hierarchy is also considered .

本文从2×2矩阵Sato理论导出多分量的KP方程族，讨论了这方程族的新的达布变换，并考虑从这方程族的约束而引出的1+1维的可积方程。

Using the matrix models of 3-dimensional Minkowski space , the author applies the integrable system theory to discuss the deformation properties and integrability on the spacelike surfaces with harmonic inverse mean curvature and the timelike surfaces with Lorentz harmonic inverse mean curvature .

利用可积系统的思想，借助三维Minkowski空间L3的矩阵模型，研究了L3中具有调和逆平均曲率的类空曲面和洛伦兹调和逆平均曲率类时曲面的可积性及其形变。

In the different magnetic field , we calculated the nearest energy space level statistic , we find that the nearest energy level spacing follow the Poisson distribution , so it is still an integrable system when applied external magnetic field for the higher symmetry circular quantum billiard system .

对不同磁场下的能量本征值进行能级统计分析发现最近邻能级间隔分布符合Poisson分布，说明对称性比较高的圆形量子台球即使在加外磁场以后仍然是可积体系。