符号计算与非线性偏微分方程精确行波解

In this paper, with the aid of the symbolic computation, a further extended tanh function method was presented. Based on the new general ansatz, many nonlinear partial differential equation（s）（NPDE（s）） can he solved. Especially, as applications, a compound KdV-mKdV equation and the Broer-Kaup equations are considered successfully, and many solutions including periodic solutions, triangle solutions, and rational solutions are obtained. The method can also be applied to other NPDEs.     

一个高维圈代数和演化方程族的可积耦合系统

An extension of the Lie algebra An-1 has been proposed [ Phys. Lett. A, 2003, 310 : 19-24 ]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra G^～. Based on the loop algebra G^～, the integrable couplings system of the NLS-MKdV equations hierarchy was obtained. As its reduction case, generalized nonlinear NLS-MKdV equations were obtained. The method proposed in this letter can be applied to other hierarchies of evolution equations.     

New exact solutions of nonlinear differential-difference equations with symbolic computation

In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete ＂ （G′/G＂）-expansion method are researched. As a result, with the aid of the symbolic computation, new hyperbolic function solution and trigonometric function solution with parameters of the Toda equation are obtained. At the same time, new envelop hyperbolic function solution and envelop trigonometric function solution with parameters of the discrete nonlinear Schro¨dinger equation with a saturable nonlinearity are obtained. This method can be applied to other nonlinear differential-difference equations in mathematical physics.     

N-soliton solutions to the modified Boussinesq equation

Searching for exact solutions to nonlinear evolution equations is a very important and interesting work in nonlinear science. In this paper, the modified Boussinesq equation is derived from the modified Gel’fand-Dikii (mG-D) system.Furthermore, we study the modified Boussinesq equation by using the bilinear method and Wronskian technique, we obtain the N-soliton solutions to the above equation.     

物理教学中类比方法的应用

在逻辑思维的方法中,常用一种“类比推理”的方法。就是根据两类事物在某些方面的相同或相似之处,进行分析、比较,把一类事物的知识推理到另一类事物中去。类比的方法是物理教学中经常采用的方法。我们可以利用学生已学过并已掌握的物理知识与另一类尚未学习过,尚未了解的知识进行比较分析,推理到另一类知识中去,从而获得新的物理知识和概念,并可培养学生抽象思维和逻辑推理的能力。     

两类新的Lie代数和它们的Liouville可积演化方程族

Based on the generalization of Lie algebra An-1,two types of new Lie algebras were worked out and the integrability of the related hierarchies of evolution equations were proved in the sense of Liouville.