组合KdV方程的显式精确解

借助计算机代数系统Mathematica，利用双曲函数法找到了组合KdV方程(Combined KdV Equation)的精确孤立波解，包括钟型孤立波解和扭结型孤立波解.在此基础上又对双曲函数法的思想进行了推广，从而获得了其更多的显式精确解，包括间断型激波解和指数函数型解.这种方法也适用于求解其他非线性发展方程(组).  

同伦分析法在求解非线性演化方程中的应用

利用同伦分析法求解了(2+1)维改进的 Zakharov-Kuznetsov方程, 得到了它的近似周期解,该解与精确解符合很好. 结果表明，同伦分析法在求解高维非线性演化方程时, 仍然是一种行之有效的方法. 同时,还对该方法进行了一定的扩展， 经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解.  

Nonlinear Wave in a Disc-Shaped Bose-Einstein Condensate

We discuss the possible nonlinear waves of atomic matter wave in a Bose-Einstein condensate. One and two of two-dimensional （2D） dark solitons in the Bose-Einstein condensed system are investigated. A rich dynamics is studied for the interactions between two solitons. The interaction profiles of two solitons are greatly different if the angle between them are different. If the angle is small enough, the maximum amplitude during the interaction between two solitons is even less than that of a single soliton. However, if the angle is large enough, the maximum amplitude of two solitons can gradually attend to the sum of two soliton amplitudes.  

An exact solution of Fisher equation and its stability

In this paper, the Fisher equation is analysed. One of its travelling wave solution is obtained by comparing it with KdV-Burgers （KdVB） equation. Its amplitude, width and speed are investigated. The instability for the higher order disturbances to the solution of the Fisher equation is also studied.  

感应电流方向的正确判定

感应电流方向的正确判定杨红娟（云南省建筑材料工业学校昆明６５０１０２）楞次定律和右手定则是确定感应电流方向的两种基本方法，下面就如何正确应用这两种方法作一讨论．１正确应用楞次定律判定感应电流的方向１．１应用楞次定律的步骤１．１．１确定穿过线圈原来磁通...  

Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap

The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.  

修正KP方程及其孤波解的稳定性

采用约化摄动法, 得到描述无磁场等离子体中离子声波传播的modified Kadomtsev- Petviashvili(mKP) 方程, 构造有限差分格式对mKP方程的一类特殊孤立波解的稳定性进行数值研究. 数值结果表明: 在两种特殊情形的初始扰动下, 该孤立波均不稳定.  

非弹性蹦球的动力学研究

对有空气阻尼的非弹性蹦球的动力学行为进行了数值模拟,通过改变控制参数V₀,蹦球的运动表现出倍周期分岔、混沌等非线性现象,采用0-1检测法和最大Lyapunov指数证实了这种现象.  

修正cKdV方程组的孤立波结构及其稳定性

利用函数展开法求解修正耦合KdV(Coupled KdV,cKdV)方程组,得到几类孤立波解,包括扭结型—钟型、双扭结型、双钟型以及双扭结—双钟型结构的单孤子解.在不同的极限情况下,这些解分别退化为修正cKdV方程的扭结状或钟状孤波解.对孤立波的稳定性进行了数值研究,结果表明:修正cKdV方程既存在稳定的孤立波解,也存在不稳定的孤立波解.  

Investigation on the resonance phenomena of multi-solitons for the （3＋1）-dimensional Kadomtsev-Petviashvili equation

In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the (3+1)-dimensional Kadomtsev--Petviashvili (KP) equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.