Kac-Moody-Virasoro Symmetry Algebra of (2+1)-Dimensional Dispersive Long-Wave Equation with Arbitrary Order Invariant

By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.

Extended Symmetry of Generalized Variable-Coefficient Kadomtsev-Petviashvili Equation

In this paper, the extended symmetry of generalized variable-coefficient Kadomtsev-Petviashvili (vcKP)equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of theextended symmetry, we can establish relation among some different kinds of vcKP equations. Thus the exact solutionsof these veKP equations can be constructed via the simple vcKP equations or constant-coefficient KP equations.

Approximate solution for the Klein Gordon-Schrdinger equation by the homotopy analysis method

The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.

Similarity Reductions of Nearly Concentric KdV Equation

基于直接方法由 Clarkson 和 Kruskal 发展了，将近同心的 Korteweg-de Vries (ncKdV ) 方程能被归结为三种类型(1+1 ) 维的可变系数部分微分方程(PDE ) 和可变系数的三种类型平常的微分方程。而且，三种类型(1+1 ) 维的可变系数 PDE 都被一些转变归结为经常的系数 PDE。

Exact Analytical Solutions in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length

在纸，概括 Riccati 方程合理扩大方法被介绍。使用方法和符号的计算，我们在场 Bose 的准确分析答案的三个家庭—有时间依赖者的爱因斯坦冷凝物内部在一个逐出的抛物线的潜力的原子相互作用。然后，二个 anlytical 解决方案的动力学被计算机模拟包括管理 Feshbach 的非线性的系数和夸张正割函数系数在一些可选的参数下面表明。

Similarity Reductions of Nonisospectral KP Equation by a Direct Method

On bases of the direct method developed by Clarkson and Kruskal [J.Math.Phys.27 (1989) 2201],the(2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1+1)-dimensional partial differential equations.We focus on solving the third type of reduction and dividing them into threesubcases,from which we obtain rich solutions including some arbitrary functions.