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 language | American English |
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Journal | Physica A: Statistical Mechanics and its Applications |
Volume | 471 |
DOIs | |
State | Published - Apr 1 2017 |
Keywords
- generalized Thomas-Fermi equation
- Emden-Fowler equation
- Abel equation
- invariant
- dynamical system
Disciplines
- Physical Sciences and Mathematics