标题： 由点对称性李代数表征的显著偏微分方程 显示英文标题

标题： Lie remarkable partial differential equations characterized by Lie algebras of point symmetries

摘要： 在逆李问题的框架下，我们给出了一些耦合李显著方程的非平凡示例，\textit{即}，这些是与它们的李点对称性相对应的微分方程类。 特别是，我们确定了由$\mathbb{R}^{n+m}$的仿射变换唯一特征化的二阶偏微分方程层次结构，以及由$\mathbb{R}^4$的射影变换李代数唯一确定的两个独立变量的三阶偏微分方程组。 显示英文摘要

摘要： Within the framework of inverse Lie problem, we give some non-trivial examples of coupled Lie remarkable equations, \textit{i.e.}, classes of differential equations that are in correspondence with their Lie point symmetries. In particular, we determine hierarchies of second order partial differential equations uniquely characterized by affine transformations of $\mathbb{R}^{n+m}$, and a system of two third order partial differential equations in two independent variables uniquely determined by the Lie algebra of projective transformations of $\mathbb{R}^4$.