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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 196, Number 3, Pages 373–389
DOI: https://doi.org/10.4213/tmf9508
(Mi tmf9508)
 

This article is cited in 7 scientific papers (total in 7 papers)

Ermakov–Pinney and Emden–Fowler equations: New solutions from novel Bäcklund transformations

S. Carilloab, F. Zulloc

a Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Università di Roma "La Sapienza". Roma, Italy
b Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Roma, Italy
c Brescia, Italy
Full-text PDF (555 kB) Citations (7)
References:
Abstract: We study the class of nonlinear ordinary differential equations $y''y= F(z,y^2)$, where $F$ is a smooth function. Various ordinary differential equations with a well-known importance for applications belong to this class of nonlinear ordinary differential equations. Indeed, the Emden–Fowler equation, the Ermakov–Pinney equation, and the generalized Ermakov equations are among them. We construct Bäcklund transformations and auto-Bäcklund transformations: starting from a trivial solution, these last transformations induce the construction of a ladder of new solutions admitted by the given differential equations. Notably, the highly nonlinear structure of this class of nonlinear ordinary differential equations implies that numerical methods are very difficult to apply.
Keywords: nonlinear ordinary differential equation, Bäcklund transformation, Schwarzian derivative, Ermakov–Pinney equation, Emden–Fowler equation.
Funding agency Grant number
Istituto Nazionale di Alta Matematica "Francesco Severi"
Instituto Nazionale di Fisica Nucleare
Sapienza Università di Roma
This research is supported by the G.N.F.M. INdAM, Sezione di Roma INFN, and the Università di Roma “La Sapienza.”
Received: 12.11.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 3, Pages 1268–1281
DOI: https://doi.org/10.1134/S0040577918090027
Bibliographic databases:
Document Type: Article
PACS: 02.30.Hq, 02.10.De, 02.30.Ik
MSC: 34A25, 37K35
Language: Russian
Citation: S. Carillo, F. Zullo, “Ermakov–Pinney and Emden–Fowler equations: New solutions from novel Bäcklund transformations”, TMF, 196:3 (2018), 373–389; Theoret. and Math. Phys., 196:3 (2018), 1268–1281
Citation in format AMSBIB
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:46
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