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International Journal of Theoretical Physics

, Volume 41, Issue 12, pp 2417–2426 | Cite as

Majorana Transformation for Differential Equations

  • S. Esposito
Article

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.

Majorana scale-invariant differential equations Emden–Fowler equations solution of the Thomas–Fermi equation 

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REFERENCES

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  4. Esposito, S., Majorana, E., Jr., van der Merwe, A., and Recami, E. (inpress). Ettore Majorana: Notebooks in Theoretical Physics, Kluwer, New York.Google Scholar
  5. Polyamin, A. D. and Zaitsev, V. F. (1995). Handbook of ExactSolutions for Ordinary Differential Equations, CRC, New York.Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • S. Esposito
    • 1
  1. 1.Dipartimento di Scienze FisicheUniversita' di Napoli “Federico II,” Complesso Universitario di Monte S. AngeloNapoliItaly

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