The Painlevй Handbook, Conte Robert, Musette Micheline

Автор: Van Assche Walter
Название: Orthogonal Polynomials and Painleve Equations
ISBN: 1108441947 ISBN-13(EAN): 9781108441940
Издательство: Cambridge Academ
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Описание: The first detailed account of the relationships between Painleve equations and orthogonal polynomials. It gives clear examples as well as proofs, and there are exercises throughout to help the reader get comfortable with the material. Useful for researchers across both fields and anyone interested in integrable systems and non-linear equations.

Автор: Alexander D. Bruno, Alexander B. Batkhin
Название: Painleve Equations and Related Topics: Proceedings of the International Conference, Saint Petersburg, Russia, June 17-23, 2011
ISBN: 3110275589 ISBN-13(EAN): 9783110275582
Издательство: Walter de Gruyter
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Описание: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Автор: Mark Adler; Pierre van Moerbeke; Pol Vanhaecke
Название: Algebraic Integrability, Painlev? Geometry and Lie Algebras
ISBN: 3642061281 ISBN-13(EAN): 9783642061288
Издательство: Springer
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Описание: In the early 70's and 80's the field of integrable systems was in its prime youth: results and ideas were mushrooming all over the world. It was during the roaring 70's and 80's that a first version of the book was born, based on our research and on lectures which each of us had given. We owe many ideas to our colleagues Teruhisa Matsusaka and David Mumford, and to our inspiring graduate students (Constantin Bechlivanidis, Luc Haine, Ahmed Lesfari, Andrew McDaniel, Luis Piovan and Pol Vanhaecke). As it stood, our first version lacked rigor and precision, was rough, dis- connected and incomplete. . . In the early 90's new problems appeared on the horizon and the project came to a complete standstill, ultimately con- fined to a floppy. A few years ago, under the impulse of Pol Vanhaecke, the project was revived and gained real momentum due to his insight, vision and determination. The leap from the old to the new version is gigantic. The book is designed as a teaching textbook and is aimed at a wide read- ership of mathematicians and physicists, graduate students and professionals.

Автор: Robert M. Conte; Micheline Musette
Название: The Painlev? Handbook
ISBN: 9400796277 ISBN-13(EAN): 9789400796270
Издательство: Springer
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Цена: 87060.00 T
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Описание: This book covers methods of building explicit solutions to nonlinear differential equations. Finding out whether the chances of success are high or low can be achieved with a powerful algorithm presented in detail called the Painleve test.

Автор: Conte Robert, Musette Micheline
Название: The Painlevй Handbook
ISBN: 3030533395 ISBN-13(EAN): 9783030533397
Издательство: Springer
Цена: 149060.00 T
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Описание: This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painleve test and shows how Painleve analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations.

Автор: Nagao Hidehito, Yamada Yasuhiko
Название: Padй Methods for Painlevй Equations
ISBN: 9811629978 ISBN-13(EAN): 9789811629976
Издательство: Springer
Цена: 60550.00 T
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Описание: The isomonodromic deformation equations such as the Painleve and Garnier systems are an important class of nonlinear differential equations in mathematics and mathematical physics. In choosing the suitable approximation problem, the linear differential equations give the Lax pair for some isomonodromic equations.

Автор: Martin A. Guest; Claus Hertling
Название: Painlev? III: A Case Study in the Geometry of Meromorphic Connections
ISBN: 3319665251 ISBN-13(EAN): 9783319665252
Издательство: Springer
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Описание:

The purpose of this monograph is two-fold: it introduces a conceptual language for the geometrical objects underlying Painleve equations, and it offers new results on a particular Painleve III equation of type PIII (D6), called PIII (0, 0, 4, -4), describing its relation to isomonodromic families of vector bundles on P1 with meromorphic connections. This equation is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears widely in geometry and physics. It is used here as a very concrete and classical illustration of the modern theory of vector bundles with meromorphic connections.

Complex multi-valued solutions on C* are the natural context for most of the monograph, but in the last four chapters real solutions on R>0 (with or without singularities) are addressed. These provide examples of variations of TERP structures, which are related to tt∗ geometry and harmonic bundles.

Автор: Decio Levi; Pavel Winternitz
Название: Painlev? Transcendents
ISBN: 0306440504 ISBN-13(EAN): 9780306440502
Издательство: Springer
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Описание: 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.

Автор: Nalini Joshi
Название: Discrete Painleve Equations
ISBN: 1470450380 ISBN-13(EAN): 9781470450380
Издательство: Mare Nostrum (Eurospan)
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Цена: 48490.00 T
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Описание: Discrete Painleve equations are nonlinear difference equations, which arise from translations on crystallographic lattices. The deceptive simplicity of this statement hides immensely rich mathematical properties, connecting dynamical systems, algebraic geometry, Coxeter groups, topology, special functions theory, and mathematical physics.This book necessarily starts with introductory material to give the reader an accessible entry point to this vast subject matter. It is based on lectures that the author presented as principal lecturer at a Conference Board of Mathematical Sciences and National Science Foundation conference in Texas in 2016. Instead of technical theorems or complete proofs, the book relies on providing essential points of many arguments through explicit examples, with the hope that they will be useful for applied mathematicians and physicists.