论文标题
标量二阶方程与低维对称组的分类：自由作用的情况
Classification of scalar second-order differential equations with low-dimensional symmetry groups: The case of free action
论文作者
论文摘要
根据定期谎言组动作的类型对微分方程的原始分类，我们提供了一个系统的程序，用于描述具有规定的对称组的部分微分方程。使用基于微分方程的所谓协变形式的新的强大代数技术，我们给出了一种有效的算法，用于构建微分方程，其对称组定期并自由地对依赖和自变量的空间自由作用。作为应用程序，我们得出了准线性标量二阶偏微分方程的完整分类，其尺寸的常规自由对称组无大于三。
Based on an original classification of differential equations by types of regular Lie group actions, we offer a systematic procedure for describing partial differential equations with prescribed symmetry groups. Using a new powerful algebraic technique based on the so-called covariant form of a differential equation, we give an effective algorithm for constructing differential equations whose symmetry groups regularly and freely act on the space of dependent and independent variables. As an application, we derive a complete classification of quasi-linear scalar second-order partial differential equations with regular free symmetry groups of dimension no greater than three.
