论文标题
标量的对称分类$ n $ th订单普通微分方程
Symmetry Classification of Scalar $n$th Order Ordinary Differential Equations
论文作者
论文摘要
我们通过他们承认的对称谎言代数来完成标量n阶的谎言对称分类，$ n \ geq 4 $，普通微分方程。众所周知，根据其拥有的对称代数，有三种类型的等式。允许点对称点的无限维度代数，具有最大八点对称和高阶的二阶方程的一阶方程，$ n \ geq 3 $，承认最大$ n + 4 $ dimensional对称代数。我们表明，$ n \ geq 4 $的第n个订单方程式不承认$ n + 3 $ dimensional Lie代数，除了$ n = 5 $，可以接纳$ sl（3，r）$代数。此外，他们可以拥有$ n + 2 $尺寸的谎言代数，从而产生非线性方程，该方程式无法通过点转换线性化。结果表明，对于$ n \ geq 5 $，只有一个这样的方程式。
We complete the Lie symmetry classification of scalar nth order, $n \geq 4$, ordinary differential equations by means of the symmetry Lie algebras they admit. It is known that there are three types of such equations depending upon the symmetry algebra they possess, viz. first-order equations which admit infinite dimensional Lie algebra of point symmetries, second-order equations possessing the maximum eight point symmetries and higher-order, $n \geq 3$, admitting the maximum $n + 4$ dimensional symmetry algebra. We show that nth order equations for $n \geq 4$ do not admit maximally an $n + 3$ dimensional Lie algebra except for $n = 5$ which can admit $sl(3, R)$ algebra. Also, they can possess an $n + 2$ dimensional Lie algebra that gives rise to a nonlinear equation that is not linearizable via a point transformation. It is shown that for $n \geq 5$ there is only one such class of equations.
