论文标题
高阶Riccati方程中的Schwarzian衍生物
Schwarzian derivative in higher-order Riccati equations
论文作者
论文摘要
Sturm-Liouville方程表示一阶Riccati方程的线性化形式。这为Schwarzian衍生物与此一阶非线性微分方程之间的联系提供了证据。对于Riccati链中的高阶方程而言，相似的连接并不明显，因为相应的线性方程式大于两个。在特别注意二阶和三阶riccati方程的过程中，我们证明了Schwarzian衍生物具有自然空间在较高的Riccati方程中。存在Schwarztan衍生物的高阶类似物。我们证明了riccati层次结构中的方程式嵌入在这些高阶导数中。
The Sturm-Liouville equation represents the linearized form of the first-order Riccati equation. This provides an evidence for the connection between Schwarzian derivative and this first-order nonlinear differential equation. Similar connection is not obvious for higher-order equations in the Riccati chain because the corresponding linear equations are of order greater than two. With special attention to the second- and third-order Riccati equations we demonstrate that Schwarzian derivative has a natural space in higher Riccati equations. There exist higher-order analogues of the Schwarztan derivative. We demonstrate that equations in the Riccati hierarchy are embedded in these higher-order derivatives.
