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Painleve Transcendents - Their Asymptotics and Physical Applications (Hardcover, 1992 ed.)
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Painleve Transcendents - Their Asymptotics and Physical Applications (Hardcover, 1992 ed.)
Series: NATO Science Series B:, 278
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The NATO Advanced Research Workshop "Painleve Transcendents, their
Asymp totics and Physical Applications," held at the Alpine Inn in
Sainte-Adele, near Montreal, September 2 -7, 1990, brought together
a group of experts to discuss the topic and produce this volume.
There were 41 participants from 14 countries and 27 lectures were
presented, all included in this volume. The speakers presented
reviews of topics to which they themselves have made important
contributions and also re sults of new original research. The
result is a volume which, though multiauthored, has the character
of a monograph on a single topic. This is the theory of nonlinear
ordinary differential equations, the solutions of which have no
movable singularities, other than poles, and the extension of this
theory to partial differential equations. For short we shall call
such systems "equations with the Painleve property." The search for
such equations was a very topical mathematical problem in the 19th
century. Early work concentrated on first order differential
equations. One of Painleve's important contributions in this field
was to develop simple methods applicable to higher order equations.
In particular these methods made possible a complete analysis of
the equation;; = f(y', y, x), where f is a rational function of y'
and y, with coefficients that are analytic in x. The fundamental
result due to Painleve (Acta Math."
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