论文标题
Schwarzian衍生物，PainlevéXXV-Mermakov方程和Bäcklund转换
Schwarzian derivative, Painlevé XXV-Ermakov equation and Bäcklund transformations
论文作者
论文摘要
重新探讨了施瓦茨衍生物在非线性普通微分方程研究中的作用。 PainlevéXXV-Mermakov方程，Ermakov方程和以正常形式的三阶线性方程所接受的解决方案和不向导是基于Schwarzian方程的溶液。从riccati方程和riccati chian的二阶元素开始，作为最简单的可线化方程示例，通过引入合适的变量更改，可以显示Schwarzian衍生产品如何代表解决方案构建的关键工具。获得了两个连接线性和非线性方程的Bäcklund变换族。给出并讨论了一些具有相关应用程序的示例。
The role of Schwarzian derivative in the study of nonlinear ordinary differential equations is revisited. Solutions and invariances admitted by Painlevé XXV-Ermakov equation, Ermakov equation and third order linear equation in a normal form are shown to be based on solutions of the Schwarzian equation. Starting from the Riccati equation and the second order element of the Riccati chian as the simplest examples of linearizable equations, by introducing a suitable change of variables, it is shown how the Schwarzian derivative represents a key tool in the construction of solutions. Two families of Bäcklund transformations which link the linear and nonlinear equations under investigation are obtained. Some examples with relevant applications are given and discussed.
