This article is cited in 16 papers

Jacobi's last multiplier, Lie symmetries, and hidden linearity: "Goldfishes" galore

M. C. Nucci

Università degli Studi di Perugia

Abstract: In addition to the reduction method, we present a novel application of Jacobi's last multiplier for finding Lie symmetries of ordinary differential equations algorithmically. These methods and Lie symmetries allow unveiling the hidden linearity of certain nonlinear equations that are relevant in physics. We consider the Einstein–Yang–Mills equations and Calogero's many-body problem in the plane as examples.

Keywords: Lie group analysis, first integral, Jacobi's last multiplier.

DOI: 10.4213/tmf6062

 English version: Theoretical and Mathematical Physics, 2007, 151:3, 851–862

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