Among the various profound but solvable models tion [41 of physics, two of the most studied are the Korteweg— d2v 1 dv 2 1 dv 1 de Vries (KdV) equation for nonlinear wave phenom—i + —(av~+ i3) + ‘yu3 +-~(2) enon [1] and the two-dimensional Ising model [2] for statistical mechanics. It has been known [3] for severwherey is the independent variable and a, j3, y, and 6 al years that a Painlevé tra...