The class of nonlinear ordinary differential equations $y^\prime\primey = F(z,y^2)$, where F is a smooth function, is studied. Various nonlinear ordinary differential equations, whose applicative importance is well known, belong to such a class of nonlinear ordinary differential equations. Indeed, the Emden-Fowler equation, the Ermakov-Pinney equation and the generalized Ermakov equations are among them. B\"acklund transformations and auto B\"acklund transformations are constructed: these last transformations induce the construction of a ladder of new solutions adimitted by the given differential equations starting from a trivial solutions. Notably, the highly nonlinear structure of this class of nonlinear ordinary differential equations implies that numerical methods are very difficulty to apply.
Ermakov-Pinney and Emden-Fowler equations: new solutions from novel Bäcklund transformations / Carillo, Sandra; Zullo, Federico. - In: THEORETICAL AND MATHEMATICAL PHYSICS. - ISSN 0040-5779. - STAMPA. - 196:3(2018), pp. 1268-1281. [10.1134/S0040577918090027]
Ermakov-Pinney and Emden-Fowler equations: new solutions from novel Bäcklund transformations
Sandra Carillo
Primo
;
2018
Abstract
The class of nonlinear ordinary differential equations $y^\prime\primey = F(z,y^2)$, where F is a smooth function, is studied. Various nonlinear ordinary differential equations, whose applicative importance is well known, belong to such a class of nonlinear ordinary differential equations. Indeed, the Emden-Fowler equation, the Ermakov-Pinney equation and the generalized Ermakov equations are among them. B\"acklund transformations and auto B\"acklund transformations are constructed: these last transformations induce the construction of a ladder of new solutions adimitted by the given differential equations starting from a trivial solutions. Notably, the highly nonlinear structure of this class of nonlinear ordinary differential equations implies that numerical methods are very difficulty to apply.File | Dimensione | Formato | |
---|---|---|---|
TAMP1268.pdf
solo gestori archivio
Note: https://link.springer.com/journal/volumesAndIssues/11232
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
505.02 kB
Formato
Adobe PDF
|
505.02 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.