非线性扩散方程的广义分离变量解

Generalized separation of variables solutions to nonlinear diffusion equations

目的构造非线性扩散方程的广义分离变量解。方法条件Lie-Bcklund对称方法。结果得到了非线性扩散方程的广义分离变量解。结论用条件Lie-Bcklund对称方法可以构造非线性扩散方程的广义分离变量解,这些解与不变子空间关系密切,有丰富的理论及实践意义。

Aim To construct generalized separation of variables solutions of nonlinear diffusion equations. Meth- ods Conditional Lie Baecklund symmetry method. Results Generalized separation of variables solutions to nonlin- ear diffusion equations are obtained. Conclusion The generalized separation of variables solutions to the nonliear diffusion equations can be constructed due to the conditional Lie Backlund symmetry method, which is of close relation to the invariant subspace, and has large numbers of theoric and practical applications.