Generalized Thomas-Fermi Equations as the Lampariello Class of Emden-Fowler Equations

Haret C. Rosu, S. C. Mancas, Stefani Mancas

Research output: Contribution to journalArticlepeer-review

Abstract

A one-parameter family of Emden–Fowler equations defined by Lampariello’s parameter p which, upon using Thomas–Fermi boundary conditions, turns into a set of generalized Thomas–Fermi equations comprising the standard Thomas–Fermi equation for p=1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas–Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.
Original languageAmerican English
JournalPhysica A: Statistical Mechanics and its Applications
Volume471
DOIs
StatePublished - Apr 1 2017

Keywords

  • generalized Thomas-Fermi equation
  • Emden-Fowler equation
  • Abel equation
  • invariant
  • dynamical system

Disciplines

  • Physical Sciences and Mathematics

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