Symmetries and differential equations

几何对称对应于几何对象的变换，使其保持不变。例如，一个正方形在绕其中心旋转90度的离散旋转下是不变的。一个圆在连续对称下是不变的，对应于绕其中心旋转任何角度。微分方程在连续对称下的不变性可以导致它的解，它转化为一个更简单的方程和/或守恒定律。通常可以确定明显的对称性，如旋转或缩放下的不变性，由于维度推理。近年来，符号计算在高速计算机上的应用使人们能够有效地利用和扩展算法来发现和应用检查分析不明显的连续对称性。这项建议涉及到寻求进一步的延期。

Geometrical symmetries correspond to transformations of geometrical objects that leave them invariant.  For example, a square is invariant under discrete rotations by 90 degrees about its centre. A circle is invariant under a continuous symmetry corresponding to rotations by any angle about its centre.  The invariance of a differential equation under a continuous symmetry can lead to its solutions, its transformation to a simpler equation and/or to conservation laws.  Often one can determine obvious symmetries such as invariance under rotations or scalings due to dimensional reasoning.  In recent years the use of symbolic computation with high speed computers allows one to effectively utilize and extend algorithms to find and apply continuous symmetries not obvious by inspectional analysis.  This proposal is concerned with finding further extensions.