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A one-parameter family of trans-series asymptotics of solutions to theDegenerate Painlev\'{e} III Equation (DP3E) are parametrised in terms of themonodromy data of an associated two-by-two linear auxiliary problem via theisomonodromy deformation approach: trans-series asymptotics for the associatedHamiltonian and principal auxiliary functions and the solution of one of thesigma-forms of the DP3E are also obtained. The actions of Lie-point symmetriesfor the DP3E are derived.

Trans-Series Asymptotics of Solutions to the Degenerate Painlev\'{e} III Equation: A Case Study