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Generalized Thomas–Fermi equations as the Lampariello class of Emden–Fowler equations

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  • Rosu, Haret C.
  • Mancas, Stefan C.

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.

Suggested Citation

  • Rosu, Haret C. & Mancas, Stefan C., 2017. "Generalized Thomas–Fermi equations as the Lampariello class of Emden–Fowler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 212-218.
    • Handle: RePEc:eee:phsmap:v:471:y:2017:i:c:p:212-218
    DOI: 10.1016/j.physa.2016.12.007
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