Although these equations were initially obtained answering a strictly mathematical
question, they appeared later in an astonishing (and growing) range of applications,
including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal
polynomials. Actually, it is now becoming clear that the Painleve transcendents
(i.e., the solutions of the Painleve equations) play the same role in nonlinear
mathematical physics that the classical special functions, such as Airy and Bessel
functions, play in linear physics. The explicit formulas relating the asymptotic
behaviour of the classical special functions at different critical points, play a
crucial role in the applications of these functions.

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