Ermakov-Pinney and Emden-Fowler equations: new solutions from novel Bäcklund transformations

Abstract

The class of nonlinear ordinary differential equations $y^{\prime \prime }y=F(z,y^2)$, 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. Bäcklund transformations and auto Bäcklund 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.

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Cited by in corpus (3)

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