Integrable time-dependent dynamical systems: Generalized Ermakov-Pinney and Emden-Fowler equations

Partha Guha, Anindya Ghose Choudhury

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We consider the integrable time-dependent classical dynamics studied by Bartuccelli and Gentile (Phys Letts. A307 (2003) 274-280; Appl. Math. Lett. 26 (2013) 1026-1030) and show its power to compute the first integrals of the (generalized) Ermakov-Pinney systems. A two component generalization of the Bartuccelli-Gentile equation is also given and its connection to Ermakov-Ray-Reid system and coupled Milne-Pinney equation has been illucidated. Finally, we demonstrate its application in other integrable ODEs, in particular, using the spirit of Bartuccelli-Gentile algorithm we compute the first integrals of the Emden-Fowler and describe the Lane-Emden type equations. A number of examples are given to illustrate the procedure.

Original languageBritish English
Pages (from-to)355-370
Number of pages16
JournalNonlinear Dynamics and Systems Theory
Volume14
Issue number4
StatePublished - 2014

Keywords

  • Emden-Fowler equation
  • Ermakov-Lewis invariant
  • Ermakov-Pinney equation
  • First integrals
  • Time-dependent harmonic oscillator

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