Volume 9, Issue Supplement 2, September 2002, Pages 1 - 9
Hidden Symmetries, First Integralsvand Reduction of Order of Nonlinear Ordinary Differential Equations
Received 1 February 2002, Available Online 2 September 2002.
- https://doi.org/10.2991/jnmp.2002.9.s2.1How to use a DOI?
- 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.
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Cite this article
TY - JOUR AU - Barbara Abraham-Shrauner PY - 2002 DA - 2002/09 TI - Hidden Symmetries, First Integralsvand Reduction of Order of Nonlinear Ordinary Differential Equations JO - Journal of Nonlinear Mathematical Physics SP - 1 EP - 9 VL - 9 IS - Supplement 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2002.9.s2.1 DO - https://doi.org/10.2991/jnmp.2002.9.s2.1 ID - Abraham-Shrauner2002 ER -