The Painleve Property: One Century Later Robert Conte

ISBN: 9781461271819

Published: November 6th 2012

Paperback

810 pages


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The Painleve Property: One Century Later  by  Robert Conte

The Painleve Property: One Century Later by Robert Conte
November 6th 2012 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, RTF | 810 pages | ISBN: 9781461271819 | 6.27 Mb

The subject this volume is explicit integration, that is, the analytical as opposed to the numerical solution, of all kinds of nonlinear differential equations (ordinary differential, partial differential, finite difference). Such equations describeMoreThe subject this volume is explicit integration, that is, the analytical as opposed to the numerical solution, of all kinds of nonlinear differential equations (ordinary differential, partial differential, finite difference).

Such equations describe many physical phenomena, their analytic solutions (particular solutions, first integral, and so forth) are in many cases preferable to numerical computation, which may be long, costly and, worst, subject to numerical errors. In addition, the analytic approach can provide a global knowledge of the solution, while the numerical approach is always local. Explicit integration is based on the powerful methods based on an in-depth study of singularities, that were first used by Poincare and subsequently developed by Painleve in his famous Lecons de Stockholm of 1895.

The recent interest in the subject and in the equations investigated by Painleve dates back about thirty years ago, arising from three, apparently disjoint, fields: the Ising model of statistical physics and field theory, propagation of solitons, and dynamical systems. The chapters in this volume, based on courses given at Cargese 1998, alternate mathematics and physics- they are intended to bring researchers entering the field to the level of present research.



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