Ermakov--Lewis invariants for a class of parametric anharmonic oscillators

Authors

  • A. Gallegos
  • H. Vargas-Rodríguez
  • J.E. Macías-Díaz

Keywords:

Damped anharmonic oscillator, generalizations of Ray--Reid systems, Ermakov--Lewis invariants

Abstract

In this letter, we investigate a general class of damped anharmonic oscillators with time-dependent coefficients. The model is a second-order ordinary differential equation in which the driving is a general function of the solution and time. Several well-known equations of mathematical physics are generalized by our model. The equation is presented then as a generalized Ray--Reid system, and an invariant of the Ermakov--Lewis type is derived next. Particular forms of this invariant are obtained for the classical harmonic oscillator and the Ermakov equation. In this form, this work opens the investigation on the determination of Ermakov--Lewis invariants of anharmonic systems.

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Published

2017-01-01

How to Cite

[1]
A. Gallegos, H. Vargas-Rodríguez, and J. Macías-Díaz, “Ermakov--Lewis invariants for a class of parametric anharmonic oscillators”, Rev. Mex. Fís., vol. 63, no. 2 Mar-Apr, pp. 162–0, Jan. 2017.

Issue

Vol. 63 No. 2 Mar-Apr (2017): Revista Mexicana de Física

Section

Articles

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.