（2+1）维耗散长波方程与(2+1)维Broer-Kaup方程新的类多孤子解

进一步拓广齐次平衡法的应用，并对关键的操作步骤进行了改进，从而简便地求出了（2+1 ）维耗散长波方程和（2+1）维Broer-Kaup方程新的类多孤子解-这种解更具有一般性，它包 含着已有文献给出的类多孤子解- 关键词： 齐次平衡法 类多孤子解 （2+1）维耗散长波方程 （2+1）维Broer-Kaup方程     

(3+1)维Nizhnik-Novikov-Veselov方程的孤子解和周期解

采用行波法约化方程,建立一种变换关系,把求解(3+1)维NizhnikNovikovVeselov(NNV)方程的解转化为求解一维非线性KleinGordon方程的解,从而得到了(3+1)维NNV方程的孤子解和周期解. 关键词： (3+1)维Nizhnik-Novikov-Veselov方程 非线性Klein-Gordon方程 孤子解 周期解     

(2+1)维非线性Burgers方程变量分离解和新型孤波结构

利用变量分离方法，获得了(2+1)维非线性Burgers方程的变量分离解.由于在Bcklund变换和变量分离步骤中引入了作为种子解的任意函数, 因而精确解中含有三个任意函数(其中一个为条件函数),适当地选择任意函数，可以获得多种形状的扭状孤波解、周期性孤子解和格子型孤波解. 关键词： 变量分离解 非线性波方程 （2+1）维     

(2+1)维Boussinesq方程的新的周期解

利用Hirota方法及Riemann theta函数得到了(2+1)维Boussinesq方程的新的周期解.在极限情况下,该周期解退化为孤子解. 关键词： Hirota方法 Riemann theta 函数 (2+1)维Boussinesq方程 周期解     

(2+1)维Broer-Kaup方程的广义dromion解结构

利用推广的齐次平衡方法,首先将(2+1)维Broer-Kaup方程线性化,然后构造出丰富的广义孤子解,包括单孤子解,单曲线孤子解,单dromion解,多dromion解。此方法直接而简单,可推广应用一大类(2+1)维非线性可积方程。     

高阶(2+1)维Broer-Kaup方程的孤波解

利用一个简单的变换将高阶(2+1)维Broer-Kaup方程变为一个简单的方程，并且结合齐次平 衡法给出了高阶(2+1)维Broer-Kaup方程的一些新的孤子解.这一方法可应用于其他非线性物 理模型. 关键词： Broer-Kaup方程 (2+1)维 孤子解 齐次平衡法     

(2+1) 维Broer-Kau-Kupershmidt方程一系列新的精确解

借助于符号计算软件Maple，通过一种构造非线性偏微分方程(组)更一般形式精确解的直接方法即改进的代数方法，求解(2+1) 维 Broer-Kau-Kupershmidt方程，得到该方程的一系列新的精确解，包括多项式解、指数解、有理解、三角函数解、双曲函数解、Jacobi 和 Weierstrass 椭圆函数双周期解. 关键词： 代数方法 (2+1) 维 Broer-Kau-Kupershmidt 方程 精确解 行波解     

sl玻色子体系在U(2l+1)→O(2l+2)过渡区的严格解

利用无穷维李代数方法得到了相互作用sl玻色子体系在U(2l+1)→O(2l+2)过渡区的能谱和波函数的严格解. 给出了该系统Bethe假定方程的数值解法.     

变系数(2+1)维Broer-Kaup系统的特殊孤子结构及孤子的裂变和湮没现象

利用改进的Riccati方程映射法，得到了变系数(2+1)维 Broer-Kaup 系统的孤波解、周期波解和变量分离解.根据得到的孤波解，构造出了系统的几种不同形状的孤子结构，研究了孤子的裂变和湮没现象. 关键词： 变系数(2+1)维 Broer-Kaup 系统 孤子结构 裂变 湮没     

一个新(2+1)维非线性演化方程的相干孤子结构

用分离变量法研究了新(2+1)维非线性演化方程的相干孤子结构.由于Bcklund变换和变量分离步骤中引入了作为种子解的任意函数,得到了新(2+1)维非线性演化方程丰富的孤子解.合适地选择任意函数,孤子解可以是solitoffs,dromions,dromion格子,呼吸子和瞬子.呼吸子不仅在幅度、形状,各峰间距离,甚至在峰的数目上都进行了呼吸. 关键词： 新(2+1)维非线性演化方程 分离变量法 孤子结构     

Inclined periodic homoclinic breather and rogue waves for the (1+1)-dimensional Boussinesq equation

A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (1+1)-dimensional Boussinesq equation is used as an example to illustrate the effectiveness of the suggested method. Rational homoclinic wave solution, a new family of two-wave solution, is obtained by inclined periodic homoclinic breather wave solution and is just a rogue wave solution. This result shows that rogue wave originates by the extreme behaviour of homoclinic breather wave in (1+1)-dimensional nonlinear wave fields.     

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.     

Variable separation solutions and new solitary wave structures to the (1+1)-dimensional equations of long-wave－short-wave resonant interaction

A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave－short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.     

The anionic chain process mechanism for reactions of perchlorofluoroethanes with nucleophiles in solution: a theoretical study

Anionic chain process mechanism (including reactions (1)–(4)) suggested by the experimental investigations for the reactions of nucleophile (CH₃O^?) with perchlorofluoroethanes CF₂ClCCl₃ ( 1 ), CF₂ClCCl₂F ( 2 ), and CF₃CCl₃ ( 3 ) in solution is examined by performing calculations using the B3LYP method and the SCIPCM (self‐consistent isodensity polarizable continuum) model for simulating solution effects. The SCIPCM‐B3LYP calculations indicate that anionic species have large solvation energies and solvation energy values for different kinds of anions are quite different, which effects changes in ΔH's for the reactions in solution. Competition between anionic hyperconjugation and solvation leads to negative ΔH values for reactions (2) from 1 and 2 in solution. Reactions (3) and (4) from 1 , 2 , and 3 in solution are predicted to be exothermic or highly exothermic. Since the ΔH values for reactions (1) and (2) from 1 and 2 in solution are negative or small positive values, the reactions of CH₃O^? with 1 and 2 in solution proceed via the anionic chain process. For 3 in solution, reactions (1) and (2) are endothermic while reactions (3) and (4) are exothermic or highly exothermic. The reactions of CH₃O^? with 3 in solution may proceed via the anionic chain process. All these conclusions are in agreement with the experimental indications for reactions of nucleophiles with 1 , 2 , and 3 in solution. Copyright © 2007 John Wiley & Sons, Ltd.     

Variable Separation Solution for （1＋1）-Dimensional Nonlinear Models Related to Schroedinger Equation

A variable separation approach is proposed and successfully extended to the (1 1)-dimensional physics models. The new exact solution of (1 1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.     

Applications of Extended Mapping Deformation Method in Two (3+1)-Dimensional Nonlinear Models

Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.     

Random integral equation formulation of a generalized Langevin equation

In this paper, the generalized Langevin equation introduced by Kubo and Mori is formulated as a random integral equation. We consider (1) the existence and uniqueness of the solution, (2) moments of the solution process, (3) a comparison theorem for solution processes, and (4) the Cauchy polygonal approximation to the solution.     

(Ti1-xNbx)5AlC4(x=0.4, 0.75, 1)固溶体系的第一性原理研究

采用第一性原理计算，通过投影缀加波(PAW)和广义梯度近似(GGA)研究三元层状化合物(MAX) Ti₅AlC₄中Nb多比例掺杂M位元素.通过计算该固溶体系的声子谱、生成焓和弹性常数，讨论了(Ti_1-xNb_x)₅AlC₄固溶体系的稳定性，得到了三种稳定的结构：(Ti_0.6Nb_0.4)₅AlC₄、(Ti_0.25Nb_0.75)₅AlC₄和Nb₅AlC₄,即(Ti_1-xNb_x)₅AlC₄(x=0.4, 0.75, 1)固溶体系.Bader电荷、局域电荷密度、态密度表明该固溶体系呈现出金属特性，且电导率随着掺杂比例的增大，电荷不断转移，电导率增强.通过计算不同掺...     

An explicit one-soliton solution of the (2+1)-dimensional generalized sine-gordon equations

The (n+1)-dimensional differential geometric generalization of the sine-Gordon equation (SGE) given by Tenenblat and Terng is solved explicitly in the casen=2 to obtain a one-soliton solution. The solution yields the soliton solution of the (1+1)-dimensional SGE in the limit as one of the three independent variables approaches infinity. However, more than one variable plays the role of time in these limits.