Quasi-Lie schemes and Emden--Fowler equations

TL;DR

This paper applies the theory of quasi-Lie schemes to Emden--Fowler equations, deriving time-dependent constants of motion and providing a new perspective on their integrability and generalizations.

Contribution

It introduces a novel application of quasi-Lie schemes to Emden equations, enabling the derivation of time-dependent constants of motion and unifying previous results.

Findings

Derived t-dependent constants of motion for specific Emden equations

Recovered known results using the quasi-Lie scheme approach

Extended the analysis to generalized Emden equations with certain conditions

Abstract

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from this new perspective. Finally some t-dependent constants of the motion for equations of Emden type satisfying certain conditions are recovered.