Jacobi’s last multiplier,Lie symmetries,and hidden linearity: “Goldfishes” galore

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. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 495–509, June, 2007.