This book is the first comprehensive treatment of Painleve
differential equations in the complex plane. Starting with a
rigorous presentation for the meromorphic nature of their
solutions, the Nevanlinna theory will be applied to offer a
detailed exposition of growth aspects and value distribution of
Painleve transcendents. The subsequent main part of the book is
devoted to topics of classical background such as representations
and expansions of solutions, solutions of special type like
rational and special transcendental solutions, Backlund
transformations and higher order analogues, treated separately for
each of these six equations. The final chapter offers a short
overview of applications of Painleve equations, including an
introduction to their discrete counterparts. Due to the present
important role of Painleve equations in physical applications, this
monograph should be of interest to researchers in both mathematics
and physics and to graduate students interested in mathematical
physics and the theory of differential equations.
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