Speaker
Dr
Dmitry Sinelshchikov
(National Research Nuclear Universtiy)
Description
In this talk we discuss applications of the generalized Sundman transformations for finding families of integrable Li\'{e}nard--type equations. Under integrable equations here we understand equations for which we can construct the general analytical solution. Employing connections, given by the generalized Sundman transformations, between Li\'{e}nard--type equations and equations of the Painleve--Gambier type we demonstrate a possibility of finding new integrable Li\'{e}nard--type equations. We consider connections between Li\'{e}nard--type equations and type I--III Painleve--Gambier equation. As a result, we obtain nine criteria for the integrability of the Li\'{e}nard--type equations. We also consider applications of this approach for finding autonomous Lagrangians, Jacobi multipliers and first integrals for Li\'{e}nard--type equations.
Primary author
Dr
Dmitry Sinelshchikov
(National Research Nuclear Universtiy)
