Solving (2+1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2+1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2+1)-dimensional sine-Poisson equation are derived in a simple manner by this technique.     

New explicit and exact solutions of the Benney--Kawahara--Lin equation

In this paper, we present a combination method of constructing the explicit and exact solutions of nonlinear partial differential equations. And as an illustrative example, we apply the method to the Benney-Kawahara-Lin equation and derive its many explicit and exact solutions which are all new solutions.     

Solving mKdV-sinh-Gordon equation by a modified variable separated ordinary differential equation method

By introducing a more general auxiliary ordinary differential equation (ODE),a modified variable separated ODE method is developed for solving the mKdV-sinh-Gordon equation.As a result,many explicit and exact solutions including some new formal solutions are successfully picked up for the mKdV-sinh-Gordon equation by this approach.     

求sine-Gordon 型方程孤波解的一种统一方法

借助于一个辅助常微分方程的解，提出了一种求sine-Gordon 型方程孤波解的统一方法，并用该法简洁地求得了三个著名的sine-Gordon 型方程，即单sine-Gordon 方程、双sine-Gordon 方程和mKdV-sine-Gordon方程的精确孤波解。     

常用坐标系中速度和加速度推导的矩阵方法

采用矩阵方法对常用坐标系中质点的速度和加速度表达式作了统一推导。     

对“求一类非线性偏微分方程解析解的一种简洁方法”一文的一点注记

利用文献中所引入的变换，将一个非线性偏微分方程化为一个非线性常微分方程，再直接求解该常微分方程，从而简洁地求得了Burgers方程的几个精确解析解.所得结果与已有结果完全符合. 关键词： 非线性偏微分方程 非线性常微分方程 解析解     

求一类非线性偏微分方程解析解的一种简洁方法

通过引入一个变换和选准试探函数，进行求偏导数运算,将非线性偏微分方程化为代数方程，然后用待定系数法确定相应的常数，最后得到其解析 解.不难看出，这种方法特别简洁. 关键词： 非线性偏微分方程 试探函数 待定系数法 解析解     

用质心速度讨论一维碰撞问题

利用质心速度讨论了两小球发生一维碰撞后的速度和动能损失。     

A simple approach to solving double sinh--Gordon equation

By introducing an auxiliary ordinary differential equation and solving it by the method of variable separation abundant types of explicit and exact solutions for the double sinh-Gordon equation are derived in a simple manner.