TY - JOUR

T1 - Integrable time-dependent dynamical systems

T2 - Generalized Ermakov-Pinney and Emden-Fowler equations

AU - Guha, Partha

AU - Choudhury, Anindya Ghose

N1 - Publisher Copyright:
© 2014 InforMath Publishing Group

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Emden-Fowler equation

KW - Ermakov-Lewis invariant

KW - Ermakov-Pinney equation

KW - First integrals

KW - Time-dependent harmonic oscillator

UR - http://www.scopus.com/inward/record.url?scp=84911410075&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84911410075

SN - 1562-8353

VL - 14

SP - 355

EP - 370

JO - Nonlinear Dynamics and Systems Theory

JF - Nonlinear Dynamics and Systems Theory

IS - 4

ER -