Transformation Properties of x'' + f_1(t)x' + f2(t)x + f3(t)x^n = 0

DOI

10.2991/jnmp.1997.4.3-4.7How to use a DOI?

Abstract

In this paper, we consider a general anharmonic oscillator of the form ¨x + f1(t) x + f2(t)x+f3(t)xn = 0, with n Q. We seek the most general conditions on the functions f1, f2 and f3, by which the equation may be integrable, as well as conditions for the existence of Lie point symmetries. Time-dependent first integrals are constructed. A nonpoint transformation is introduced by which the equation is linearized.

Copyright

© 2006, 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/).

Download article (PDF)

TY  - JOUR
AU  - Norbert Euler
PY  - 1997
DA  - 1997/09/01
TI  - Transformation Properties of x'' + f_1(t)x' + f2(t)x + f3(t)x^n = 0
JO  - Journal of Nonlinear Mathematical Physics
SP  - 310
EP  - 337
VL  - 4
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1997.4.3-4.7
DO  - 10.2991/jnmp.1997.4.3-4.7
ID  - Euler1997
ER  -