一般变系数耗散长水波方程的精确解

By using the homogeneous balance principle(HBP),we derive a B■cklund trans- formation(BT)to the generalized dispersive long wave equation with variable coefficients. Based on the BT,we give many kinds of the exact solutions of the equatioh,such as,single solitary solutions,multi-soliton solutions and generalized exact solutions.     

推广的F -展开法及变系数KdV和mKdV的精确解

该文首先推广了新近提出的F -展开法,利用该方法导出了变系数KdV和mKdV方程 的类椭圆函数解;并在极限的情况下,得到变系数KdV和 mKdV方程变波速和变波长的类孤子解以及其他形式解.     

应用F展开法求KdV方程的周期波解

提出了求非线性数学物理演化方程周期波解的F展开法,该方法可看作最近提出的扩展的Jacobi椭圆函数展开方法的浓缩.直接利用F展开法而不计算Jacobi椭圆函数,我们可同时得到著名的KdV方程的多个用Jacobi椭圆函数表示的周期波解.当模数m→1 时,可得到双曲函数解(包括孤立波解).     

Applications of F-expansion method to the coupled KdV system

An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.     

4-四氢喹啉酮的合成及发光性能

对喹吖啶酮结构改造合成了新型结构荧光体4-四氢喹啉酮,对其吸收光谱及荧光光谱进行了研究,发现该化合物的吸收峰及荧光发射峰随溶剂极性的增加而不断红移,表明荧光来源于分子内激发态电荷转移发光.该化合物在固态即显示荧光,表明经结构改造后,消除了喹吖啶酮类的固态荧光猝灭效应.4-四氢喹啉酮结构简单,易于合成和结构修饰.这对于寻找新的主体荧光发射材料具有重大意义.     

THE TRAVELING WAVE SOLUTIONS AND APPROXIMATE SOLUTIONS FOR BOUSSINESQ EQUATIONS

First, all possible traveling wave solutions of the Boussinesq equations in shallow water theory are discussed. It is shown that these solutions are periodic waves, convex solitary waves and concave solitary waves. Second, by using a reductive perturbation method, shallow water equation with a small damping term have been reduced to a single KdV-Burgers equation, from which the approximate solution of the original equations can be expressed.     

SYMMETRIES， BāCKLUND TRANSFORMATIONS AND BOUNDARY－INITIAL VALUE PROBLEMS FOR NONLINEAR CHROMATOGRAPH

ＳＹＭＭＥＴＲＩＥＳ，Ｂ■ＣＫＬＵＮＤＴＲＡＮＳＦＯＲＭＡＴＩＯＮＳＡＮＤＢＯＵＮＤＡＲＹ－ＩＮＩＴＩＡＬＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＮＯＮＬＩＮＥＡＲＣＨＲＯＭＡＴＯＧＲＡＰＨＹＥＱＵＡＴＩＯＮＷａｎｇＭｉｎｇｌｉａｎｇ（王明亮）（Ｄｅｐｔ．ｏ...     

Burgers型方程初值问题解的稳定性及孤波解

本文证明Burgers型方程初值问题的解在L₂意义上的稳定性、唯一性;给出该方程存在扭状孤波解的条件及求扭状孤波解的方法。并指出Burgers型方程不存在钟状孤波解。     

高效液相色谱法测定茯苓皮的指纹图谱

本文用正交设计优化茯苓皮的超声提取条件,并有效提取了茯苓皮药材内的主要成分三萜类物质,同时利用高效液相色谱法(HPLC)建立了提取物的液相指纹图谱。实验考察了不同提取溶剂、提取条件对提取工艺的影响;确立了最佳色谱条件,得到了茯苓皮中24种总提取物的指纹图;同时对10种不同产地的茯苓皮药材进行分析,标定了17个共有峰。研究结果表明,HPLC指纹图谱方法重现性好,稳定可靠,可用于控制茯苓皮中三萜成分的质量。     

The periodic wave solutions for the generalized Nizhnik－Novikov－Veselov equation

The periodic wave solutions expressed by Jacobi elliptic functions for the generalized Nizhnik－Novikov－Veselov equation are obtained using the F-expansion method proposed recently. In the limiting cases, the solitary wave solutions and other types of travelling wave solutions for the system are obtained.