中文摘要：

利用条件Lie-Bcklund对称研究非线性反应扩散方程组。首先对方程组进行分类,得到了方程组允许的不变子空间等价于方程的高阶Lie-Bcklund对称,并通过例子构造方程组定义在多项式、三角函数及指数函数类型的不变子空间上的广义分离变量解。

英文摘要：

The conditional Lie-Bcklund symmetry（CLBS）approach is applied to study the reaction-diffusion system.It is shown that the system of equation admit a class of invariant subspaces,which is equivalent to a kind of higher-order conditional Lie-Bcklund symmetries of the system.As a result,generalized separable variable solutions defined on the polynomial,trigonometric and exponential invariant subspace are constructed for some resulting equation.