Ermakov-Lewis Invariants and Reid Systems

S.C. Mancas; Haret C. Rosu; Stefani Mancas

doi:10.1016/j.physleta.2014.05.008

Ermakov-Lewis Invariants and Reid Systems

S.C. Mancas, Haret C. Rosu, Stefani Mancas

Research output: Contribution to journal › Article › peer-review

Abstract

Reid's m th-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy.

Original language	American English
Journal	Physics Letters A
Volume	378
DOIs	https://doi.org/10.1016/j.physleta.2014.05.008
State	Published - Jun 13 2014

Keywords

Ermakov-Lewis invariant
Reid system
Emden-Fowler equation
Abel equation
parametric solution

Disciplines

Applied Mathematics

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title = "Ermakov-Lewis Invariants and Reid Systems",

abstract = " Reid's m th-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy.",

keywords = "Ermakov-Lewis invariant, Reid system, Emden-Fowler equation, Abel equation, parametric solution",

author = "S.C. Mancas and Rosu, {Haret C.} and Stefani Mancas",

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T1 - Ermakov-Lewis Invariants and Reid Systems

AU - Mancas, S.C.

AU - Rosu, Haret C.

AU - Mancas, Stefani

PY - 2014/6/13

Y1 - 2014/6/13

N2 - Reid's m th-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy.

AB - Reid's m th-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy.

KW - Ermakov-Lewis invariant

KW - Reid system

KW - Emden-Fowler equation

KW - Abel equation

KW - parametric solution

UR - https://commons.erau.edu/publication/644

U2 - 10.1016/j.physleta.2014.05.008

DO - 10.1016/j.physleta.2014.05.008

M3 - Article

SN - 1873-2429

VL - 378

JO - Physics Letters A

JF - Physics Letters A

ER -

Ermakov-Lewis Invariants and Reid Systems

Abstract

Keywords

Disciplines

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