Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations
Mancas, Stefan C
Rosu Barbus, Haret-Codratian
"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."
KeywordsGeneralized Thomas-Fermi equation
CitationHaret C. Rosu, Stefan C. Mancas, Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations, Physica A: Statistical Mechanics and its Applications, Volume 471, 2017, Pages 212-218.
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