back to author index
   
title:
 
Hidden Symmetries, First Integralsvand Reduction of Order of Nonlinear Ordinary Differential Equations
publication:
 
JNMP
volume-issue:   9 - Supplement 2
pages:   1 - 9
ISSN:
  1402-9251
DOI:
  doi:10.2991/jnmp.2002.9.s2.1 (how to use a DOI)
author(s):
 
Barbara ABRAHAM-SHRAUNER
publication date:
 
September 2002
abstract:
 
The reduction of nonlinear ordinary differential equations by a combination of first integrals and Lie group symmetries is investigated. The retention, loss or even gain in symmetries in the integration of a nonlinear ordinary differential equation to a first integral are studied for several examples. The differential equations and first integrals are expressed in terms of the invariants of Lie group symmetries. The first integral is treated as a differential equation where the special case of the first integral equal to zero is examined in addition to the nonzero first integral. The inverse problem for which the first integral is the fundamental quantity enables some predictions of the change in Lie group symmetries when the differential equation is integrated. New types of hidden symmetries are introduced.
copyright:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
full text: