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
zullo, federico
2018-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.