论文标题
Riccati和Abel链的等效类别和线性化
Equivalence classes and Linearization of the Riccati and Abel chain
论文作者
论文摘要
在广义的Riccati和Abel序列中，解决了按点转换线性化的问题，不超过第四次。特别表明，来自链条的非线性三阶和第四阶方程都无法通过任何点变换线性化。然后找到了从链中的任意顺序方程的等价转换的谎言伪组，以及转换参数函数的表达式。考虑了发现的等效转换组的重要亚组，并展示了一些相关的等效类别。
The problem of linearization by point transformations is solved for equations in the generalized Riccati and Abel chain of order not exceeding the fourth. It is shown in particular that nonlinear third order and fourth order equations from the chain are not linearizable by any point transformations. The Lie pseudo-group of equivalence transformations for equations of arbitrary orders from the chain are then found, together with expressions for the transformed parameter functions. An important subgroup of the group of equivalence transformations found is considered and some associated equivalence classes are exhibited.
