Closed-form solutions of the Thomas-Fermi in heavy atoms and the Langmuir-blodgett in current flow ODEs in mathematical physics
type: Item
instance of: scholarly article
title: Closed-form solutions of the Thomas-Fermi in heavy atoms and the Langmuir-blodgett in current flow ODEs in mathematical physics
zbMATH Open document ID: 1394.34029
DOI: 10.1155/2015/721637
author: T. I. Zarmpoutis
author: Ioannis H. Stampouloglou
author: E. E. Theotokoglou
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Two kinds of second-order nonlinear, ordinary differential equations (ODEs) appearing in mathematical physics are analyzed in this paper. The first one concerns the Thomas-Fermi (TF) equation, while the second concerns the Langmuir-Blodgett (LB) equation in current flow. According to a mathematical methodology recently developed, the exact analytic solutions of both TF and LB ODEs are proposed. Both of these are nonlinear of the second order and by a series of admissible functional transformations are reduced to Abel's equations of the second kind of the normal form. The closed form solutions of the TF and LB equations in the phase and physical plane are given. Finally a new interesting result has been obtained related to the derivative of the TF function at the limit.
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 6927083
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/721637
OpenAlex ID: W1482560993
Wikidata QID: Q59119035
cites work: Q3292729
cites work: Q5521729
cites work: Q4890882
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description: scientific article; zbMATH DE number 6927083