互反型高维可积Kaup-Newell系统

可积系统研究是物理和数学等学科的重要研究课题.然而,通常的可积系统研究往往被限制在(1+1)维和(2+1)维,其原因是高维可积系统极其稀少.最近,我们发现利用形变术可以从低维可积系统导出大量的高维可积系统.本文利用形变术,将(1+1)维的Kaup-Newell(KN)系统推广到(4+1)维系统.新系统除了包含原来的(1+1)维的KN系统外,还包含三种(1+1)维KN系统的互反形式.模型也包含了许多新的(D+1)维(D≤3)的互反型可积系统.(4+1)维互反型KN系统的Lax可积性和对称可积性也被证明.新的互反型高维KN系统的求解非常困难.本文仅研究(2+1)维互反型导数非线性薛定谔方程的行波解,并给出薛定谔方程孤子解的隐函数表达式.     

具有广义Virasoro对称代数的(3+1)维Painlevé可积模型

寻找高维可积模型(特别是3+1维可积模型)是非线性物理中的一个非常重要的问题.建立了一种利用广义Virasoro对称性的高维实现首先找到了一些(3+1)维Virasoro可积模型,并证明(3+1)维Virasoro可积模型均具有KacMoodyVirasoro对称代数.更进一步,利用WeissTaborCarnevale的奇性分析方法,证明了其中一个Virasoro可积模型也是Painlev啨可积的. 关键词： 广义Virasoro代数 Painlevé性质 (3+1)维可积模型     

具有物理背景的高维Painlevé可积模型

提出了一种求解任意维数非线性模型的“M?bious”变换下不变的渐进展开方法,并可同时获得许多新的与原模型有着相同维数的Painlevé可积模型.取(2+1)维KdV-Burgers(KdVB)方程和Kadomtsev-Petviashvili(KP)方程为具体例子,获得了一些新的具有Painlevé性质的高维“M?bious”变换下不变的方程及原模型的近似解.在某些特殊情况下,某些近似解可以成为精确解 关键词： 高维可积模型 “M?bious”不变 近似方法     

具有物理背景的高维Painlev可积模型

提出了一种求解任意维数非线性模型的“M bious”变换下不变的渐进展开方法 ,并可同时获得许多新的与原模型有着相同维数的Painlev啨可积腜?.取 (2 1)维KdV Burgers(KdVB)方程和Kadomtsev Petviashvili(KP)方程为具体例子 ,获得了一些新的具有Painlev啨性质的高维“Ｍ bious”变换下不变的方程及原模型的近似解 .在某些特殊情况下 ,某些近似解可以成为精确解     

具有物理背景的高维Painleve可积模型

提出了一种求解任意维数非线性模型的“Moebious”变换不变的渐进展开方法，并可同时获得许多新的与原模型有着相同维数的Painleve可积模型，取（2＋1）维Kdv-Burgers(KdVB)方程和Kadomtsev-Petviashvili(KP）方程为具体例子，获得了一些新的具有Painleve性质的高维“Moebiours”变换下不变的方程及模型近似解,顺某些特殊情况下，某些近似解可以成为精确解。     

一类高维耦合的非线性演化方程的简单求解

利用一个简单的变换，一类高维耦合的非线性演化方程可以被约化为一低维的简单方程，将已有的求解法应用于简单方程，十分简捷的获得了原方程大量的精确解. 关键词： 非线性耦合方程 精确解 tanh函数方法     

高维微分-差分模型的Virasoro对称子代数，多线性变量分离解和局域激发模式

寻找高维可积模型是非线性科学中的重要课题.利用无穷维Virasoro对称子代数［σ(f₁),σ(f₂)］=σ(f′₁f₂-f′₂f₁)和向量场的延拓结构理论，能够得到各种高维模型.选取一些特殊的实现，可以给出具有无穷维Virasoro对称子代数意义下的高维微分可积模型.把该方法推广到微分-差分模型上，构造出具有弱多线性变量分离可解性的(3+1)维类Toda晶格.另外，该模型的一个约化方程为具有多线性变量分离可解性的(2+1)维特殊Toda晶格.连续运用对称约化方法可以得到此特殊Toda晶格的一个(1+1)维约化方程具有多线性变量分离可解性.因为得到的精确解里含有低维任意函数，从而可以构造出丰富地局域激发模式，如dromion解，lump解，环孤子解，呼吸子解，瞬子解，混沌斑图和分形斑图等等. 关键词： Virasoro代数 微分-差分模型 变量分离 局域激发模式     

扩展的形变映射方法和(2+1)维破裂孤子方程的新解

扩展的形变映射方法应用于非线性物理模型的研究， 获得了(2+1)维破裂孤子方程的新解, 合适地选择任意函数，可以获得该模型的丰富的局域和非局域的相干结构，这里仅揭示(2+1)维破裂孤子方程(1)和(2)的周期型新孤波结构. 关键词： 形变映射方法 (2+1)维破裂孤子方程 孤波结构     

一类S-mKdV方程族及其扩展可积模型

由loop代数的一个子代数出发，构造了一个线性等谱问题，再利用屠格式计算出了一类Liouvelle意义下的可积系统及其双Hamilton结构，作为该可积系统的约化，得到了著名的Schrdinger方程和mKdV方程，因此称该系统为S-mKdV方程族.根据已构造的的子代数，又构造了维数为5的loop代数的一个新的子代数，由此出发设计了一个线性等谱形式，再利用屠格式求得了S-mKdV方程族的一类扩展可积模型.利用这种方法还可以求BPT方程族、TB方程族等谱系的扩展可积模型.因此本方法具有普遍应用价值.最后作为特例，求得了著名的Schrdinger方程和mKdV方程的可积耦合系统.     

基于变系数3+1维三次-五次复金兹堡-朗道方程的亮孤子及混合孤子传输特性

变系数3+1维三次-五次复金兹堡-朗道(CGL)方程作为光孤子传输模型,不仅用五次项解释了现有模型所没有的物理意义,还拥有高维系统较低维系统更为丰富的非线性动力学特性.本文利用修正的Hirota方法,得到了变系数3+1维三次-五次CGL方程的解析孤子解.通过对非线性系数和光谱滤波项选取特定的参数,得到了一种特殊的混合孤子.分别讨论了改变非线性、光谱滤波和线性损失参数以及其他参数对孤子传输特性的影响,实现了对亮孤子和混合孤子传输的有效控制.本文结论对高维CGL系统在理论和实验研究方面具有一定的参考价值.     

HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS

A conformal invariant asymptotic expansion approach to solve any nonlinear integrable and nonintegrable models with any dimension is proposed. Many new Painlevé integrable models with the same dimension can be obtained at the same time. Taking the (2+1)-dimensional KdV-Burgers (KdVB) equation, (3+1)-dimensional Zabolotskaya-Khokhlov and Kudomtsev-Petviashvili (ZKKP) equation as concrete examples, we obtain some new higher dimensional conformal invariant models with Painlevé property and the approximate solutions of these models. In certain special cases, some of the approximate solutions become exact.     

A Variable Separation Approach to Solve the Integrable and Nonintegrable Models:Coherent Structures of the (2 + 1)-Dimensional KdV Eqnation

We study the localized coherent structures ofa generally nonintegrable (2 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.     

A New Asymptotic Approach to Solve Nonlinear Evolution Equations

A conformal-invariant asymptotic expansion approach to solve any nonlinear integrable and nonintegrable models with any dimensions is proposed. Taking the compound KdV-Burgers (cKdVB) equation and the KdV-Burgers (KdVB) equation as concrete examples,we obtain many new conformal-invariant models with Painleve' property and the approximate solutions of the cKdVB and KdVB equations. In some special cases, the approximate solutions become exact.     

Exact Solutions of the Coupled KdV system via a Formally Variable Separation Approach

Most of the nonlinear physics systems are essentially nonintegrable.There in no very doog analytical approach to solve nonintegrable system.The variable separation approach is a powerful method in linear physics.In this letter,the formal variable separation approach is established to solve the generalized nonlinear mathematical physics equation.The method is valid not only for integrable models but also for nonintegrable models.Taking a nonintegrable coupled KdV equation system as a simple example,abundant solitary wave solutions and conoid wave solutions are revealed.     

Effect of rare fluctuations on the thermalization of isolated quantum systems

We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In particular, we investigate the prerequisites for thermalization, focusing on the statistical properties of the time-averaged density matrix and of the expectation values of observables in the final eigenstates. We find that eigenstates, which are rare compared to the typical ones sampled by the microcanonical distribution, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some nonintegrable systems of finite size, such as the Bose-Hubbard model. We stress the importance of finite size effects for the thermalization of isolated quantum systems and discuss two scenarios for thermalization.     

Numerical simulation of a solitonic gas in KdV and KdV–BBM equations

The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV equation. We extend this analysis to non-integrable KdV–BBM type models. Some high resolution numerical results are presented in both integrable and nonintegrable cases. Moreover, the free surface elevation probability distribution is shown to be quasi-stationary. Finally, we employ the asymptotic methods along with the Monte Carlo simulations in order to study quantitatively the dependence of some important statistical characteristics (such as the kurtosis and skewness) on the Stokes–Ursell number (which measures the relative importance of nonlinear effects compared to the dispersion) and also on the magnitude of the BBM term.     

Transport in quasi one-dimensional spin-1/2 systems

We present numerical results for the spin and thermal conductivity of one-dimensional (1D) quantum spin systems. We contrast the properties of integrable models such as the spin-1/2 XXZ chain against nonintegrable ones such as frustrated and dimerized chains. The thermal conductivity of the XXZ chain is ballistic at finite temperatures, while in the nonintegrable models, this quantity is argued to vanish. For the case of frustrated and dimerized chains, we discuss the frequency dependence of the transport coefficients. Finally, we give an overview over related theoretical work on intrinsic and extrinsic scattering mechanisms of quasi-1D spin systems.     

形式变量分离法及一般Hirota-Satsuma方程新的精确解

将形式变量分离方法推广应用于一个不可积的一般Hirota-Satsuma方程,得到了一些新的孤波解和周期波解. 关键词：     

Interface Shape and Concentration Distribution in Crystallization from Solution under Microgravity

The usual formally variable separation approach is valid only for completely integrable models. In this paper, we extend the method to a nonintegrable generalized Hirota-Satsuma equations. Some new exact solitary wave solutions and periodic wave solutions of the equations are also obtained.