Asymptotic stability of solitary wave solutions to the regularized long-wave equation

We study the asymptotic stability of solitary wave solutions to the regularized long-wave equation (RLW) in . RLW is an equation which describes the long waves in water. To prove the result, we make use of the monotonicity of the local H¹-norm and apply the Liouville property of (RLW) as in Merle and Martel (J. Math. Pures Appl. 79 (2000) 339; Arch. Rational Mech. Anal. 157 (2001) 219).     

试论苏洵"风水相遭"说对写作学的启示

苏洵在《仲兄字甫说》中提出的“风水相遭”说具有丰富的内涵,对现代写作学有着重要的启示意义,即写出平淡自然的学作品有两种可遵循的方法。     

欧阳修《试笔》成书考

欧阳修《试笔》是平时信笔所书,后人摭集其手迹而成。《试笔》包括诗、文、书、画等各方面的内容,是了解欧阳修文艺思想的重要资料。本文对《试笔》的流传及成书进行详细考辨,纠正了前人的一些讹误。     

The variational iteration method for solitary patterns solutions of gBBM equation

We consider solitary patterns solutions of generalized Benjamin–Bona–Mahony equations (shortly gBBM). The variational iteration method (shortly VIM) is applied for the numerical solution subject to appropriate initial condition. The numerical solutions of our model equation are calculated in the form of convergence power series with easily computable components. The VIM performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability.     

A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation

In this paper, we employ the boundary-only meshfree method to find out numerical solution of the classical Boussinesq equation in one dimension. The proposed method in the current paper is a combination of boundary knot method and meshless analog equation method. The boundary knot technique is an integration free, boundary-only, meshless method which is used to avoid the known disadvantages of the method of fundamental solution. Also, we use the meshless analog equation method to replace the nonlinear governing equation with an equivalent nonhomogeneous linear equation. A predictor-corrector scheme is proposed to solve the resulted differential equation of the collocation. The numerical results and conclusions are obtained for both the ‘good’ and the ‘bad’ Boussinesq equations.     

微扰非线性薛定谔方程的孤子解

非线性薛定谔方程作为描述波包在弱非线性色散介质中传播的普遍方程。在光纤维中脉冲在皮秒范围内的传输可以用微扰非线性薛定谔方程来描述。文章采用实指数方法并借助Mathematica符号计算软件编程求其孤子解。     

论谭嗣同思想产生的社会基础和理论渊源

谭嗣同是戊戌维新派的杰出代表 ,是戊戌变法时为追求真理而勇敢牺牲的伟大的爱国者 ,同时也是中国近代史上比较有影响力的思想家。本文主要探讨谭嗣同思想产生的社会基础和理论渊源。     

Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

二维RLW方程和二维SRLW方程的显式精确解

本文讨论了二维RLW方程和二维SRLW方程孤立波解的性态，通过直接积分的方法求出了这两个方程的显式精确孤立波解，并通过选取初始条件的方法求出了二维RLW方程和二维SRLW方程的另一类精确行波解．     

New Peakons and Periodic Peakons of the Modified Camassa-Holm Equation

In this paper, we obtain new peakon and periodic peakon solutions to a modified Camassa-Holm equation. We change the modified Camassa- Holm equation into a planar system. Then the first integral and algebraic curves of this system are obtained. By using the first integral and algebraic curves, a new peakon solution is given by hyperbolic function. Moreover, some new periodic peakons are given by elliptic functions and triangle functions.