A one-parameter family of trans-series asymptotics as and i for solutions of the degenerate Painlev III equation (DP3E), u^ () = (u^ () ) ^{2}u () - u^ () + 1 (-8 (u () ) ^2 + 2ab) + b^2u (), where 1, a C, and b R 0, are parametrised in terms of the monodromy data of an associated first-order 2 2 matrix linear ODE via the isomonodromy deformation approach: trans-series asymptotics for the associated Hamiltonian and principal auxiliary functions and the solution of one of the -forms of the DP3E are also obtained. The actions of various Lie-point symmetries for the DP3E are derived.
A. Vartanian (Fri,) studied this question.