随机发展方程适度解的存在唯一性(Ⅱ)

讨论如下Hilbert空间中的半线性随机发展方程的Cauchy问题 dy(t)=[Ay(t) f(t,y(t))]dt G(t,y(t))dw(t) y(O)=V_u的适度解的存在唯一性,在更一般的条件下,得到了该问题的适度解的存在唯一性。     

关于混合型多项式Hammerstein积分方程正解迭代求法

本文给出了混合型多项式Ｈａｍｍｅｒｓｔｅｉｎ积分方程正解的迭代求法，并将所得结果应用到二阶非线性常微分方程的边值问题     

线性双向联想存储器

提出了一个线性双向联想存储器的模型，一组有限个向量对由一线性算子建立起双向联想关系，此线性算于是一个网络的联结权重矩阵。该权矩阵由最小二乘法决定。由权矩阵的解导出一特殊类型的Ｌｙａｐｕｎｏｖ矩阵方程．本文提供了这种Ｌｙａｐｕｎｏｖ矩阵方程的解。     

Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg-Landau equation with variable coefficients

We consider an inhomogeneous optical fiber system described by the generalized cubic complex Ginzburg-Landau (CGL) equation with varying dispersion, nonlinearity, gain (loss), nonlinear gain (absorption) and the effect of spectral limitation. Exact chirped bright and dark soliton-like solutions of the CGL equation were found by using a suitable ansatz. Furthermore, we analyze the features of the solitons and consider the problem of stability of these soliton-like solutions under finite initial perturbations. It is shown by extensive numerical simulations that both bright and dark soliton-like solutions are stable in an inhomogeneous fiber system. Finally, the interaction between two chirped bright and dark soliton-like pulses is investigated numerically.     

A rational approximation and its applications to nonlinear partial differential equations on the whole line

An orthogonal system of rational functions is discussed. Some inverse inequalities, imbedding inequalities and approximation results are obtained. Two model problems are considered. The stabilities and convergences of proposed rational spectral schemes and rational pseudospectral schemes are proved. The techniques used in this paper are also applicable to other problems on the whole line. Numerical results show the efficiency of this approach.     

一类函数方程的稳定性及微商配置解

本文对一类重要的函数方程建立解稳定性定理,提出微商配置解,证明了收敛性.     

A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

相对论性无自旋粒子在Hartmann势场中运动的精确解

在标量势等于矢量势的条件下,本文获得了具有Hartmann型势的Klein-Gordon方程的精确解.给出了束缚态的精确的能谱方程和归一化的径向波函数,对于散射态,获得了按“k/2π标度”归一化的径向波函数和相移的解析计算公式.讨论了散射振幅的解析性质和波函数、能谱方程以及相移的非相对论近似.     

浅析二阶齐次线性变系数微分方程的一个可积类型

本文讨论了二阶齐次线性变系数微分方程的特殊形式，给出了这种微分方程的一个可积类型．     

变系数非线性方程的Jacobi椭圆函数展开解

把Jacobi椭圆函数展开法扩展并应用到求解变系数的非线性演化方程,比较方便地得到新的解析解 关键词： Jacobi椭圆函数 变系数非线性方程 类椭圆余弦波解 类孤子解