New 2x2-matrix linear problems for the Painleve equations

Abstract: We construct 2x2-matrix linear problems with a spectral parameter for the Painleve equations I-V by means of the degeneration processes from the elliptic linear problem for the Painleve VI equation. These processes supplement the known degeneration relations between the Painleve equations with the degeneration scheme for the associated linear problems. The degeneration relations constructed in this paper are based on the trigonometric, rational, and Inozemtsev limits.