Partial integrability of the anharmonic oscillator

DOI

10.2991/jnmp.2007.14.3.11How to use a DOI?

Abstract

We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u ′′ + g1 (x)u ′ + g2 (x)u + g3 (x)u n + g4 (x) = 0, n real. Its physical applications range from the atomic Thomas-Fermi model to Emden gas dynamics equilibria, the Duffing oscillator and numerous dynamical systems. The present work is an overview which includes and generalizes all previously known results of partial integrability of this oscillator. We give the most general two conditions on the coefficients under which a first integral of a particular type exists. A natural interpretation is given for the two conditions. We compare these two conditions with those provided by the Painlev ́e analysis.

Copyright

© 2007, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Robert Conte
PY  - 2007
DA  - 2007/10/01
TI  - Partial integrability of the anharmonic oscillator
JO  - Journal of Nonlinear Mathematical Physics
SP  - 462
EP  - 473
VL  - 14
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2007.14.3.11
DO  - 10.2991/jnmp.2007.14.3.11
ID  - Conte2007
ER  -