Padé approximations for Painlevé I and II transcendents (Q1034480)

The author shows, that the Painlevé I and II equations can be transformed into a form to which the Fair-Luke algorithm is applicable to find the Padé approximate solutions. It appears that the numerical implementation of this algorithm works fast even on the PC of initial level. By this way, the author received the distribution of poles for the well-known Ablowitz- Segur and Hastings-McLeod solutions of the Painlevé II equation and suggested some conjectures. The algorithm allows checking other analytic properties of the Painlevé transcendents, such as the asymptotic behaviour at infinity in the complex plane.