Quasi-Lie schemes and Emden--Fowler equations

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.

References in corpus (5)

• Superposition rules, Lie theorem and partial differential equations
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• Applications of Lie systems in dissipative Milne--Pinney equations
• Integrability of Lie systems and some of its applications in physics
• A geometric approach to integrability conditions for Riccati equations