Hidden Symmetries, First Integrals and Reduction of Order of Nonlinear Ordinary Differential Equations
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 example...
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| Veröffentlicht in: | Journal of nonlinear mathematical physics 2002, Vol.9, p.1-9 |
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| container_title | Journal of nonlinear mathematical physics |
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| creator | Abraham-Shrauner, Barbara |
| description | 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. |
| doi_str_mv | 10.2991/jnmp.2002.9.s2.1 |
| format | Article |
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| issn | 1402-9251 1776-0852 |
| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; SpringerLink Journals - AutoHoldings |
| subjects | Integrals Inverse problems Lie groups Mathematical analysis Nonlinear differential equations Reduction |
| title | Hidden Symmetries, First Integrals and Reduction of Order of Nonlinear Ordinary Differential Equations |
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