KdV方程的延拓结构

利用外微分形式系统和Lie代数表示理论提出了求解非线性波方程Lax对的延拓结构理论,该方法是构造非线性波方程Lax对的系统最有效的方法.其关键在于如何给出延拓代数的具体表示,如微分算子表示或矩阵表示.如果一个非线性波方程具有非平凡的延拓代数,则称其延拓代数可积,本篇论文主要利用延拓结构理论,讨论KdV方程的解,同时给出...     

微分特征列法在拟微分算子和Lax表示中的应用

微分特征列法用于拟微分算子和非线性发展方程Lax表示的计算.首先,利用微分特征列法和微分带余除法计算拟微分算子的逆和方根,由于不必求解常微分方程组,并将解代入,因此,使得计算得以简化.其次,利用微分特征列法,约化从广义Lax方程和Zakharov-Shabat推出的非线性偏微分方程,并得到相应的非线性发展方程.在Mathematica计算机代数系统上,编写了相关程序,从而可以利用计算机辅助完成一些非线性发展方程Lax表示的计算.     

关于AKNS族和一个耦合的MKdV族的规范等价可积系统与r-矩阵

得到了一个新的耦合的MKdV族．通过规范变换，首次从AKNS族中得到耦合的MKdV族的Lax表示、可积系与约束流；利用Lax表示，构造了耦合MKdV族的约束流的γ-矩阵，同时也给出了该方程族约束流的第二组守恒积分与对合性．     

发展方程族Lax表示的广义结构*

本文给出非线性发展方程族的一个生成格式(该格式包含了保谱族与非保谱族作为其两个特殊情况),并提供该格式下发展方程族Lax表示的广义结构.最后,作为应用,我们讨论了Levi族发展方程.     

关于广义Toda方程的r-矩阵方法

本文利用 r-矩阵及 Lie 双代数方法研究广义 Toda 方程的 Lax 表示,完全可积性以及解曲线的性质.     

Bell多项式在经典Boussinesq方程中的应用

本文借助于Bell多项式研究经典Boussinesq方程,将其转换成Hirota双线性形式,构造了带参数的B(a)cklund变换,进而重新导出了其Lax表示.     

KdV方程及其相应的约束条件

§1.引言 众所周知,许多著名的孤子方程有两种换位表示。1968年,Lax引入算子L,M,其中L是联系谱问题的算子,M是相应于演化方程的算子:     

Fokas-Lenells方程的代数几何解

从一个给定的谱问题出发,利用Lenard梯度序列推导出Fokas-Lenells方程.随后,这个方程被分解为可解的常微分方程.基于Lax矩阵的有限阶展开,引入了椭圆坐标,从而,流可以在Abel-Jacobi坐标下被拉直.最后,利用Riemann θ函数得到了Fokas- Lenells方程的代数几何解的表示.     

多分量退化的CH型方程的可积性及其解（英文）

主要研究多分量退化的含有立方项的CH型方程,并证明了其可积性:Lax表示,双哈密顿结构,以及递推算子.特别地,得到了一个退化的两分量的Novikov方程,并给出了其有限个拐点的奇性解.     

应用(1/G)-展开法求解五阶KdV方程

本篇论文首次提出(1/G) -展开法,用于求解非线性演化方程的行波解.将该法应用于五阶KdV方程的求解,当参数满足一定条件时,该方程可化为Sawada-Kotera (SK)方程、Caudrey-Dodd-Gibbon(CDG)方程、Kaup-Kupershmidt (KK)方程、Lax方程和Ito方程.其解可被表示为...     

Design of a small conversational system

The main features of a time-sharing system for a minicomputer are outlined. An interpretive language LAX plays a central role in the system both as a base for the languages seen by the user and for implementing part of the system. The system is open-ended, new subsystems can be plugged in easily, and a variety of error and interrupt behavior can be obtained.     

Summands of Stable Equivalences of Morita Type

A stable equivalence of Morita type between two finite dimensional algebras with no separable summand will be shown to restrict to stable equivalences of Morita type between their summands. We will apply this to prove that stable equivalence of Morita type preserves self-injectivity of algebras and the property of being symmetric.     

Π_1空间上J-正常算子的J-酉等价

对于Π_1空间上J-正常算子的J-酉等价问题进行讨论.针对不同情况,给出了Π_1空间上两个J-正常算子J-酉等价的充要条件.这将有助于研究Π_1空间上交换J-von Neumann代数之间的J-酉等价.     

Suborbits and group extensions of flows

Given a pair of an ergodic measured discrete equivalence relationR and a subrelationS ⊂R of finite index, a classification of the inclusion up to orbit equivalence will be discussed. In case of amenable and type III₀ relations, the orbit equivalence classes of inclusions will be completely classified in terms of a collection of a subgroupH and a normal subgroupG ₀ of a finite groupG and an ergodic group (G/G ₀) extension of a nonsingular flow. This is a generalization of Krieger’s theorem by which orbit equivalence classes of single relations were classified. Due to this result, essential type III inclusions will be made clear. Supported by the Japan Ministry of Education, Grant-in-Aid for Scientific Research No. (C)07640223. An erratum to this article is available at .     

Weighted blowups and mirror symmetry for toric surfaces

This paper explores homological mirror symmetry for weighted blowups of toric varietes. It will be shown that both the A-model and B-model categories have natural semi-orthogonal decompositions. An explicit equivalence of the right orthogonal categories will be shown for the case of toric surfaces.     

Von Neumann equivalence and group exactness

We will show that group exactness is a von Neumann equivalence invariant. This result generalizes the previously known fact stating that group exactness is stable under measure equivalence and W*-equivalence.     

An elementary Green imprimitivity theorem for inverse semigroups

Semigroup Forum - A Morita equivalence similar to that found by Green for crossed products by groups will be established for crossed products by inverse semigroups. More precisely, let S be an...     

Involutive moving frames

By combining the ideas of Cartan's equivalence method and the method of the equivariant moving frame for pseudo-groups, we develop an efficient method for solving a wide variety of equivalence problems. The key is a pseudo-group analog of the classic result that characterizes congruence of submanifolds in Lie groups in terms of equivalence of the Lie group's Maurer-Cartan forms. This result, when combined with the fundamental recurrence formulas for the moving frame for pseudo-groups, will allow for a hybrid equivalence method that computationally improves on and illuminates both its progenitors.     

Differentiable difference approximations for nonlinear initial-value problems.I

This paper deals with the approximation of nonlinear initial-value problems by difference methiods. in the Present part I The basic definitions and concepts are presented and equivalence theorems for stability and continuous convergenc are proved. Here, The differentiability condition (d) and the boundedness condition (Bp) are of fundamental siginificance. the latter is one of the equivalent characterizations of stability. The equivalence theorems for stability and continuous convergence include characterizations by means of locally uniform two-sided Lipschitz conditions and tow-sided discertization error estimates. At the end of part I a generalized of the concept of stable convergence of Dahlquist [2] and Torng [16] is proved to series of equivalent conditions convergence. in part II the above results will yields a series of equivalent conditions for the concepts of weak stability and conditions convergence of certain order. Moreover, further convergence concepts for semi-homogeneous methods will be studied, and hyperbolic and parawbolic example will be treated     

Equivalence Relation between Initial Values and Solutions for Evolution p-Laplacian Equation in Unbounded Space

In this paper,an equivalence relation between the ω-limit set of initial values and the ω-limit set of solutions is established for the Cauchy problem of evolution p-Laplacian equation in the unbounded space Yσ(RN).To overcome the difficulties caused by the nonlinearity of the equation and the unbounded solutions,we establish the propagation estimate and the growth estimate for the solutions.It will be demonstrated that the equivalence relation can be used to study the asymptotic behavior of solutions.