微分方程的Majorana变换
Majorana transformation for differential equations
摘要：
我们提出了一种方法，减少满足给定的比例关系的常微分方程（马约拉纳尺度不变方程）的顺序。我们还开发了这种方法的一个变体，旨在减少低阶方程的非线性程度。这些方法的一些应用进行，特别是，我们表明，二阶Emden-Fowler方程可以转化为一阶Abel方程。这里提出的工作是一个推广的方法所使用的马约拉纳，以解决费米子-费米方程。
英文摘要：
We present a method for reducing the order of ordinary differential equations satisfying a given scaling relation (Majorana scale-invariant equations). We also develop a variant of this method, aimed to reduce the degree of non-linearity of the lower-order equation. Some applications of these methods are carried out and, in particular, we show that second-order Emden-Fowler equations can be transformed into first-order Abel equations. The work presented here is a generalization of a method used by Majorana in order to solve the Thomas-Fermi equation.
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