Majorana transformation for differential equations

Details Majorana transformation for differential equations Majorana transformation for differential equations

2002-04-19

arxiv.org/abs/math-ph/0204040v1

Int.J.Theor.Phys. 41 (2002) 2417-2426

Physics

Mathematical Physics

RevTex, 8 pages

Scientific paper

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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