Majorana Transformation for Differential Equations |
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Authors: | S. Esposito |
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Affiliation: | (1) Dipartimento di Scienze Fisiche, Universita' di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Via Cinthia, I-80126 Napoli, Italy |
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Abstract: | 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 nonlinearity 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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Keywords: | Majorana scale-invariant differential equations Emden– Fowler equations solution of the Thomas– Fermi equation |
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