拟线性双曲组一类非局部混合初-边值问题的半整体C1解

在研究拟线性弦振动方程带第三类边值问题的精确边界能控性时,出现了拟线性双曲组一类非局部混合初-边值问题.论文先证明该类非局部混合问题局部C1解的存在惟一性,并考察其存在高度的性质,进而利用一致先验估计证明半整体C1解的存在惟一性,并以此为基础研究相应问题的精确边界能控性,最后为便于应用,将论文的结论写成了可化约方程组的情形.     

玻色化方法在超对称可积系统的应用

利用玻色化方法可以避免超对称可积系统中反对易费米场带来的计算困难. 本文以N=1超对称mKdVB系统为例, 利用玻色化方法, 将其转化为只有玻色场的耦合系统. 应用标准的WTC方法, 证明了该耦合系统具有Painlevé性质. 运用Painlevé截断方法, 可以得到玻色化后超对称mKdVB系统的非局域对称. 为了求解与非局域对称相关的Lie第一性原理, 引入新的场将玻色化后系统拓展为更大的系统. 通过引入新的场, 该非局域对称局域化为Lie点对称. 因此, 可以利用Lie点对称约化方法研究拓展后的系统, 得到超对称mKdVB系统的孤子与其他孤波相互作用解.     

Soliton molecules and the CRE method in the extended mKdV equation

The soliton molecules of the(1+1)-dimensional extended modified Korteweg–de Vries(mKdV)system are obtained by a new resonance condition, which is called velocity resonance. One soliton molecule and interaction between a soliton molecule and one-soliton are displayed by selecting suitable parameters. The soliton molecules including the bright and bright soliton, the dark and bright soliton, and the dark and dark soliton are exhibited in figures 1–3, respectively.Meanwhile, the nonlocal symmetry of the extended mKdV equation is derived by the truncated Painlevé method. The consistent Riccati expansion(CRE) method is applied to the extended mKdV equation. It demonstrates that the extended mKdV equation is a CRE solvable system. A nonauto-B?cklund theorem and interaction between one-soliton and cnoidal waves are generated by the CRE method.     

New interaction solutions and nonlocal symmetry of an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form

The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method. The nonlocal symmetries are localized to the Lie point symmetry by introducing new auxiliary dependent variables. The finite symmetry transformation and the Lie point symmetry for the prolonged system are solved directly. Many new interaction solutions among soliton and other types of interaction solutions for the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form can be obtained from the consistent condition of the consistent tanh expansion method by selecting the proper arbitrary constants.     

基于Retinex理论与概率非局部均值的红外图像增强方法

针对传统红外图像增强算法中细节模糊及过度增强的问题,提出了一种基于Retinex理论与概率非局部均值相结合的红外图像增强方法.首先通过单尺度Retinex方法调整图像中过暗与过亮部分的灰度级;然后利用概率非局部均值对图像进行分解处理得到基本层与细节层,对基本层采用直方图均衡化拉伸对比度,对细节层采用非线性函数进行增强;最后,将不同层次的结果融合得到对比度与细节增强的红外图像.用该方法对多组不同场景的红外图像进行仿真实验,并将其与多种增强方法进行主、客观对比分析,结果表明所提方法在红外图像的细节及对比度增强方面都获得了更好的效果.     

Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space

In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations with nonlocal conditions in Banach space. The existence of mild solutions and some conditions for approximate controllability of these non-autonomous impulsive evolution equations are given by using the Krasnoselskii''s fixed point theorem, the theory of evolution family and the resolvent operator. In particular,the impulsive functions are supposed to be continuous and the nonlocal item is divided into Lipschitz continuous and completely bounded. An example is given as an application of the results.     

向列相液晶中强非局域空间光孤子的实验观察

通过实验对向列相液晶中的非局域空间光孤子的传输进行了研究。理论上基于非线性的液晶孤子传输方程,采用高斯形式的试探解,得到了孤子传输的解析解,以及对液晶中的非局域孤子和Snyder等提出的强非局域孤子模型的结果进行了比较。实验上,观察了空间光孤子在向列相液晶中的传输,找到了不同束宽下空间光孤子的临界功率。比如束宽为2μm时临界功率为2.0mW。观察了向列相液晶中空间光孤子的弛豫过程,并注意到液晶分子的响应时间长达几秒钟,液晶中的孤子形成速度较慢。     

Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions

In this paper, we present a numerical approach to a class of nonlinear reaction-diffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.     

具有非局部时滞的扩散Nicholson苍蝇方程的波前解

研究了具有非局部时滞的扩散Nicholson苍蝇方程,其中时滞由一个定义在所有过去时间和整个一维空间区域上的积分卷积表示.当时滞核是强生成核时,根据线性链式技巧和几何奇异扰动理论,获得了小时滞时波前解的存在性.