APPLICATION OF UNIFORM ASYMPTOTICS METHOD TO ANALYZING THE ASYMPTOTIC BEHAVIOUR OF THE GENERAL FOURTH PAINLEVÉ TRANSCENDENT

We use the uniform asymptotics method proposed by A. P. Bassom et al. (1998) to study the general fourth Painlevé transcendent, find a group of its asymptotics and the corresponding monodromic data, and prove its existence and “uniqueness.” 1