We use the known relationship between the Lagrangian and Jacobi’s last multiplier of second-order ordinary differential equations to determine two first integrals and their Noether symmetries for the Fuch’s solution of Painlevé VI after finding two Lagrangians in addition to known Hamiltonian given by Malmquist. The general solution follows and we show it to be the same as given by Fuchs.
NUCCI, M.C., P. G. L. LEACH (2007). Fuch's solution of Painleve' VI equation by means of Jacobi last multiplier. JOURNAL OF MATHEMATICAL PHYSICS, 48(1), 013514-1-013514-7 [10.1063/1.2426417].
Fuch's solution of Painleve' VI equation by means of Jacobi last multiplier
NUCCI, Maria Clara;
2007
Abstract
We use the known relationship between the Lagrangian and Jacobi’s last multiplier of second-order ordinary differential equations to determine two first integrals and their Noether symmetries for the Fuch’s solution of Painlevé VI after finding two Lagrangians in addition to known Hamiltonian given by Malmquist. The general solution follows and we show it to be the same as given by Fuchs.File in questo prodotto:
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