含弛豫项的广义光学Bloch方程的近似解

本文用叠代法求得了含弛豫项的广义光学Bloch方程的近似解。与计算机给出的数值积分解的比较表明,一阶叠代解具有足够好的精度。由此得出了上能级占有几率随时间变化的解析表达式及多光子吸收、Bloch-Siegert频移等有用结果。     

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u = u^k（δu）^α

This paper undertakes a systematic treatment of the low regularity local wellposedness and ill-posedness theory in H^s and H^s for semilinear wave equations with polynomial nonlinearity in u and δu. This ill-posed result concerns the focusing type equations with nonlinearity on u and δtu.     

NONLINEAR EVOLUTION SYSTEMS AND GREEN’S FUNCTION

In this paper, we will introduce how to apply Green’s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen’s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green’s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.     

非自包含不动点定理及其在投入产出方程中的应用

本文利用拓扑度方法建立一个非自包含不动点定理,并利用它们对一类非线性(连续型)投入产出方程加以研究,得到相应的存在性与连续性结果.     

一类二阶带阻尼项的不稳定型差分方程的振动性与非振动性

应用分类讨论方法和分析方法,讨论了一类广泛的二阶非线性差分方程解的振动性与非振动性,推广并改进了已有文献中的相关结果.     

齐次平衡法求解非线性SCHR(O)DINGER方程

用齐次平衡法求解了非线性Schr(O)dinger方程iφt+a1φxx+a2φ-a3|φ|2φ=0,并讨论了解与方程系数的关系.     

动弦中点轨迹方程求法归类剖析

在圆锥曲线中，求满足一定条件的动弦的中点轨迹方程是解析几何中比较棘手的问题，解题的方法较多，但运算过程往往比较繁琐复杂，学生往往难以人手，本文采用引进参数的办法对此类问题归类分析，以便学生从中掌握其解题的基本思想和解题规律。