基于吴方法的确定和分类(偏)微分方程古典和非古典对称新算法理论

本文基于微分形式吴方法,给出了确定和分类微分方程古典和非古典对称的统一的机械化算法理论.用该理论克服了在传统Lie算法中存在的缺陷,使确定和分类对称更系统和直接,从而扩大了对称方法的应用范围.这也是吴方法在微分领域中一个新的应用.

A new algorithmic theory for determining and classifying classical and non-classical symmetries of partial differential equations

In this article, based on differential form Wu＇s method, unified mechanical algorithmic theories for determining and classifying classical, non-classical symmetries of partial differential equations are proposed. Some theoretical and algorithmic deficiencies commonly encountered in Lie＇s algorithm are overcame by the theories. The algorithms make the determination and classification of symmetry become more direct and systematic and extend the range of applications of Lie＇s algorithm. This is also a new application of Wu＇s method in the field of differential equations.