一维非自治经典谐振子的精确解析解

一维时间相关的经典谐振子是一个SU(1,1) 非自治经典系统,物理上十分有用,而数学上难于得到其精确解析解. 首次把新颖的代数动力学方法用于经典动力学系统,得到了这个模型的一般精确解;当时间相关的弹性系数为某些初等函数时,给出了精确解的解析形式. 这是关于这一问题的重要结果. 从精确解出发,推导出最近文献中提出的"解析近似解",并指出该近似解的适用条件.     

Global nonautonomous Schrodinger flows on Hermitian locally symmetric spaces

In this paper, we consider the global existence of one-dimensional nonautonomous (inhomogeneous) Schrodinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of the nonautonomous (inhomogeneous) Schrodinger flow from S1 into a Hermitian locally symmetric space admits a unique global smooth solution, and then we address the global existence of the Cauchy problem of inhomogeneous Heisenberg spin ferromagnet system.     

Nonautonomous bright solitons and soliton collisions in a nonlinear medium with an external potential

We present exact bright multi-soliton solutions of a generalized nonautonomous nonlinear Schrdinger equation with time-and space-dependent distributed coefficients and an external potential which describes a pulse propagating in nonlinear media when its transverse and longitudinal directions are nonuniformly distributed.Such solutions exist in certain constraint conditions on the coefficients depicting dispersion,nonlinearity,and gain(loss).Various shapes of bright solitons and interesting interactions between two solitons are observed.Physical applications of interest to the field and stability of the solitons are discussed.     

具有垂直传染非自治SIR传染病模型的持久性和灭绝性

通过对一类具有垂直传染的非自治SIR传染病模型的研究，在较弱的条件下，不仅得到了疾病一致强持久（即疾病流行）的充分必要条件．而且给出了疾病消失的判别准则．     

具有Ⅳ类功能反应的非自治捕食系统的持续性和周期解

本文讨论了一类具有HollingⅣ类功能反应的非自治捕食系统,利用Brouwer不动点定理和构造Liaponov函数的方法．得到该系统永久持续生存和存在唯一全局稳定的周期解的充分条件．     

Differential equations with almost periodic or conditionally periodic coefficients: Recurrence and reducibility

Recurrence of an individual trajectory of a linear nonautonomous differential equation on a compact Lie group for the case of an almost periodic or conditionally periodic dependence of the right-hand side on time is proved. The relation between recurrence and reducibility is examined.Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 229–237, August, 1998.This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00378 and No. 96-15-96072.     

Threshold conditions for a discrete nonautonomous SIRS model

In this paper, a discrete nonautonomous SIRS epidemic model is studied. The model is constructed by applying a nonstandard finite difference scheme. Under weaker assumptions, the sufficient and necessary conditions on the permanence and strong persistence of the disease and the sufficient condition on the extinction of the disease are established. In order to illustrate our theoretical analysis, some numerical simulations are included in the end. Copyright © 2014 John Wiley & Sons, Ltd.     

微分方程零解的弱渐近稳定与不稳定的判定定理

给出了平凡解弱渐近稳定定义及在已知导函数 d Vdt负定的情况下 ,通过 V( t,x)函数的符号性质来判定微分方程平凡解的弱渐近稳定性与不稳定性 ,并举例说明定理的应用 .     

弱D-拉回指数吸引子的存在性

主要研究弱D-拉回指数吸引子的存在性.首先讨论了弱D-拉回指数吸引子与非紧性测度之间的关系,其次,建立了弱D-拉回指数吸引子存在性的一般方法,最后证明了外力项具有指数增长速度的反应扩散方程在H_0~1(Ω)中存在弱D-拉回指数吸引子.     

一类高阶非线性非自治动态方程的动力学性质

研究了时间测度链T上的一类高阶非线性非自治动态方程的动力学性质,利用时间测度链理论,结合一些经典不等式,得到了该系统新的动力学性质,并举例说明了本文定理的重要性。