Ermakov-Lewis Invariants and Reid Systems

Abstract

Reid's m'th-order generalized Ermakov systems of nonlinear coupling constant alpha 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\geq 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

8 pages, published version

References in corpus (2)

• Dynamical invariants for quantum control of four-level systems
• A nonlinear superposition rule for solutions of the Milne--Pinney equation

Cited by in corpus (10)

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• Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator