Variable Separation for (1+1)-Dimensional Nonlinear Evolution Equations with Mixed Partial Derivatives

We present basic theory of variable separation for (1+1)-dimensional nonlinear evolution equations with mixed partial derivatives. As an application, we classify equations u_xt=A(u,u_x)u_xxx+B(u,u_x) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples.     

Pitch tournament designs and other BIBDs—existence results for the case ν = 8n

A pitch tournament is a resolvable or near resolvable(ν,8,7) BIBD that satisfies certain criteria in addition to theusual condition that ν ≡ 0 or 1 (mod 8). Here we establish that for the case ν = 8n the necessary condition forpitch tournaments is sufficient for all n > 1615, with at most 187 smaller exceptions. This complements our earlier study of the ν = 8n + 1 case, where we established sufficiency for all n > 224, with at most 28 smaller exceptions. The four missing cases for (ν,8,7) BIBDs are provided, namely ν∈{48,56,96,448}, thereby establishing that the necessary existence conditions are sufficient without exception. Some constructions for resolvable designs are also provided, reducing the existence question for (ν,8,7) RBIBDs to 21 possible exceptions. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 334–356, 2001     

General Symmetry Approach to Solve Variable—Coefficient Nonlinear Equations

After considering the variable coefficient of a nonlinear equation as a new dependent variable,some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach.Taking the nonlinear Schrodinger equation as a concrete example,the method is recommended in detail.     

样条状态变量法分析扁球壳的动力响应

基于瞬时变分原理与样条函数理论,建立扁球壳的动力方程,引入样条参数及其对时间的导数作为状态变量,导出状态方程,对空间域,采用样条有限元法,对时间域,采用现代控制论中的状态空间法,此外,建立了一种状态变量的递推计算格式,在计算过程中,不解线性方程组,也不需采用解耦技术,只要作矩阵运算,可直接算出动力响应量,文末给出的数值算例表明本文方法是可靠 与有效的。     

线性回归模型中自变无选择的逐步回归方法及其相合性研究

线性回归模型的建立,一个很重要的过程就是自变元的选择,它直接决定着模型的优劣。本文给出了“宜取回归方程”的逐步回归方法,在一组适当的条件下,证明了这种方法的强相合性。     

区间运算和静力区间有限元

用均值和离差两参数表征区间变量的不确定性,根据区间运算规则,论证了区间变量的运算特性.将区间分析和有限元方法相结合,提出了非概率不确定结构的一种区间有限元分析方法.将区间有限元静力控制方程中n自由度不确定位移场特征参数的求解归结为求解一2n阶线性方程组.实例分析表明文中方法是有效和可行的.     

多重尺度法应用于变厚度开顶扁球壳在复合载荷下的非线性稳定问题

利用改进多重尺度法研究了大几何参数的变厚度的具有刚性中心的开顶扁球壳,在复合载荷作用下的非线性稳定问题,求得了扁壳几何参数k值较大时,本问题的一致有效的渐近解,并进行了余项误差估计。     

The Solitary Waves for Cubic-Quintic Nonlinear Schrödinger Equation with Variable Coefficients

The cubic-quintic nonlinear Schrödinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schrödinger equation with variable coefficients (vCQNLS) are derived with the aid of a set of subsidiary high-order ordinary differential equations (sub-equations for short). The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.     

Variable separation solutions and new solitary wave structures to the （l＋l）-dimensional Ito system

A variable separation approach is proposed and extended to the (1+1)-dimensional physics system. The variable separation solution of (1+1)-dimensional Ito system is obtained. Some special types of solutions such as non-propagating solitary wave solution, propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.     

General Solution and Localized COherent Soliton Structures of the （2＋1）—Dimensional Generalized Davey—Stewarson Equations

In this paper,the variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized Davey-Stewarson equations:iqt 1/2(qxx=qyy) (R S)q=0,Rx=-σ/2|q|y^2,Sy=-σ/2|q|2/x.Applying a special Baecklund transformation and introducing arbitrary functions of the seed solutions.and abundance of the localized structures of this model is derived,By selceting the arbitrary functions appropriately,some special types of localized excitations such as dromions,dromion lattice,breathers,and instantons are constructed.