Approximate symmetry reduction for perturbed nonlinear SchrSdinger equation

We investigate the one-dimensional nonlinear SchrSdinger equation with a perturbation of polynomial type. The approximate symmetries and approximate symmetry reduction equations are obtained with the approximate symmetry perturbation theory.     

Painleve Integrability of Nonlinear SchrSdinger Equations with both Space- and Time-Dependent Coefficients

We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger （NLS） equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal＇s simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations.     

与Euler函数φ(n)有关的非线性方程的正整数解

在Euler函数φ(n)的性质的基础上,利用整数分解的方法证明了对任意的正整数m,n,非线性方程φ(mn)=aφ(m)+bφ(n)+c~2(a,b,c为勾股数且gcd(a,b,c)=1)当(a,b,c)=(3,4,5),(5,12,13),(7,24,25)时无正整数解,并证明了当a,b为任意的一奇一偶,c为任意的奇数,且满足a~2+b~2=c~2,gcd(a,b)=1,2|b时,方程无正整数解.     

用观察法求二阶变系数齐线性方程的非零特解

主要用观察法求二阶变系数齐线性方程的非零特解.首先推广了欧拉方程和另外一个关于求非零特解的结论,其次在已有结果的情形外增添一些可用观察法求特解的情形.     

A nonclassical LIL for geometrically weighted series in Banach space

Let {X, Xn ; n ≥ 0} be a sequence of independent and identically distributed random variables, taking values in a separable Banach space (B,||·||) with topological dual B* . Considering the geometrically weighted series ξ(β) =∑∞n=0βnXn for 0 β 1, and a sequence of positive constants {h(n), n ≥ 1}, which is monotonically approaching infinity and not asymptotically equivalent to log log n, a limit result for(1-β2)1/2||ξ(β)||/(2h(1/(1-β2)))1/2 is achieved.     

求解非线性方程根四阶收敛的迭代格式

提出了求解非线性方程根新的四阶收敛迭代方法,新方法每次迭代只需要两次函数计算,一次一阶导数值计算,效能指数达到1.587.通过几个数值算例来解释该方法的有效性.     

分光光度法工作曲线不符线性关系的探讨 II: 关于在等色点波长测量

光度法工作曲线不成线性关系的情况多数是由体系存在逐级配合物所致, 为获得线性关系, 有人提出在两逐级配合物的主要等色点波长测量, 认为这样可以避免同时生成第二配合物的影响, 但没有深入的理论分析。本文通过实验与理论分析, 证明此法在多数情况下仅可改善线性关系, 但不能得到直线, 经进一步研究, 找到了这个问题的另外解决办法。     

二维周期系数线性微分方程的特征指数

给出利用系数直接判定二维周期系数线性微分方程特征指数符号的若干结论．     

一类非线性方程孤波解的直接积分法

通过直接积分求出了一类非线性方程的孤波解。