Liouville可积方程是数学中重要的可积系统之一，它被广泛应用于动力学、李群理论等领域。Liouville可积系统具有独特的性质，使得其方程具有解析解，并且其相空间中的轨道是有限维的。在动力学系统中，Liouville可积系统对于理解系统的稳定性和行为具有重要意义。在李群理论中，Liouville可积系统能够提供对于李代数和李群结构的深刻洞察。这些方程的研究不仅仅停留在数学理论层面，还广泛应用于物理学和工程学的实际问题中。通过深入理解Liouville可积系统的特性，人们能够更好地探索和解决复杂问题。
Liouville可积,Liouville integrable
1)Liouville integrableLiouville可积
1.A new hierarchy of Lax integrable andLiouville integrablegeneralized Hamiltonian equations;一族新Lax和Liouville可积广义Hamilton方程
2.One class of new loop algebra and itsLiouville integrable hierarchy of evolution equations;一类新的圈代数和它的Liouville可积演化方程族
3.Starting from a isospectral problem and basing on the basis number and commutative relations of loop algerba,we propose a type ofLiouville integrable system and its bi-Hamiltonian structure by the use of Tu Guizhang s model.当位势选取特殊函数时,得到了著名的Schrodinger方程,广义MkdV方程,热传导方程和耦合的Burgers方程及其Hamiltonian结构,并证明方程是Liouville可积的。
英文短句/例句
1.A hierarchy of integrable systems of Liouville and its Bi-Hamiltonian structures;一族Liouville可积系及其双Hamilton结构
2.Hamiltonian Structures and Liouville Integrability of a New Soliton Hierarchy一族孤子方程的Hamilton结构及Liouville可积性
3.Hamiltonian Structure and Liouville Integrability of a New Soliton Hierarchy;一族新的孤子方程的Hamilton结构及Liouville可积性
4.Riemann-Liouville Fractional Calculus and the Proving of the Properties;Riemann-Liouville分数阶微积分及其性质证明
5.Solvability of a class of high order Sturm-Liouville boundary value problems一类高阶Sturm-Liouville边值问题的可解性
6.Solvability of a class of nonlinear Sturm-Liouville boundary value problems;一类非线性Sturm-Liouville边值问题的可解性(英文)
7.Positive Solutions of Singular Nonlinear Sturm-Liouville Problems;可分离变量奇异非线性Sturm-Liouville问题的正解
8.Research on Sturm-Liouville Eigenvalue ProblemsSturm-Liouville特征值问题
9.Feature Value of Sturm-Liouville;常型Sturm-Liouville问题的特征值
10.The Variational Problem of A Sturm-Liouville Boundary Value EquationSturm-Liouville方程的变分问题
11.Inverse Sturm-Liouville Problems with Indefined Weighted Functions不定型Sturm-Liouville逆问题
12.HENSTOCK INTEGRAL AND ITS CLASS OF INTEGRABLE FUNCTION;HENSTOCK积分及其可积函数类
13.THE COUNTABLE ADDITIVITY OF SET-VALUED INTEGRALS AND F-VALUED INTEGRALS集值积分与模糊值积分的可列可加性
14.A kind of Henstock ( but not Lebesgue ) integrable function;一类Henstock可积而非Lebesgue可积的函数
15.The Liouville Property and the Energy Growth Property of F-Harmonic Maps;F-调和映照的Liouville性质和能量增长性质
16.Liouville Theorem and Green Function for Degenerate Elliptic Equations;退化椭圆型方程的Liouville定理及Green函数
17.Multiplicity of Positive Solutions to Impulsive Equations with Sturm-Liouville Boundary Value Problems;具脉冲Sturm-Liouville边值问题的多重正解
18.The Existence of the Solutions to the Sturm-Liouville Boundary Value Problem in Banach Space;Banach空间Sturm-Liouville边值问题解的存在性
相关短句/例句
Liouville integrabilityLiouville可积
1.By means of the trace identity the Hamilton structure of the equations is constructed and theLiouville integrability is also proved.引入一个新的离散等谱特征值问题,导出相应的非线性微分-差分方程族,利用迹恒等式建立了方程族的Hamilton结构,证明了方程族是Liouville可积的。
2.TheLiouville integrability for the corresponding lattice system is demonstrated.通过离散的零曲率表示导出了一个基于离散的矩阵谱问题的典型晶格孤子方程,同时证明了相应的晶格系统是Liouville可积的,进一步通过一个直接的办法给出了相应晶格系统的无穷多守恒律。
3.Further,itsLiouville integrability is also given.给出一个2×2谱问题及其相应的孤子方程,并利用此孤子族的Lenard算子对的性质,证明了该系统是具有Bi-Hamilton结构的广义Hamilton系统,进一步给出其Liouville可积性的证明。
3)Liouville integrabilityLiouville可积性
1.This paper has listed some discrete integrable systems by the discrete zero curvature representation, and, some research such as theLiouville integrability, infinitely many conservation laws and integrable couplings have been investigated.本文利用离散的零曲率表示的方法构造了几个新的离散的可积系统,并对离散的可积系统的Liouville可积性、无穷多守恒律、可积耦合系统作了研究。
4)Liouville integrable systemLiouville可积系
5)Conserved denityLiouville完全可积
6)the completely integrable system in the Liouville senseLiouville完全可积系
延伸阅读
积积1.长久累积。
