TY  - JOUR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Solution of the equivalence problem for the third Painleve equation
JF  - Journal of mathematical physics
N2  - We find necessary conditions for a second order ordinary differential equation to be equivalent to the Painleve III equation under a general point transformation. Their sufficiency is established by reduction to known results for the equations of the form y ' = f (x, y). We consider separately the generic case and the case of reducibility to an autonomous equation. The results are illustrated by the primary resonance equation.
Y1  - 2015
U6  - https://doi.org/10.1063/1.4905383
SN  - 0022-2488
SN  - 1089-7658
VL  - 56
IS  - 1
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Differential invariants of a class of Lagrangian systems with two degrees of freedom
JF  - Journal of mathematical analysis and applications
KW  - Equivalence
KW  - Differential invariant
KW  - Euler-Lagrange equations
Y1  - 2014
U6  - https://doi.org/10.1016/j.jmaa.2013.08.015
SN  - 0022-247X
SN  - 1096-0813
VL  - 410
IS  - 2
SP  - 733
EP  - 749
PB  - Elsevier
CY  - San Diego
ER  -