The Isomonodromic Deformation Method in the Theory of Painleve Equations
Author: Alexander R. Its
Publisher: Springer
Published: 2006-11-14
Total Pages: 318
ISBN-13: 3540398236
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The Isomonodromic Deformation Method in the Theory of Painlevé Equations
Author: Alexander R. Its
Publisher: Springer
Published: 1986
Total Pages: 338
ISBN-13:
DOWNLOAD EBOOKThe Painlevé Property
Author: Robert Conte
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 828
ISBN-13: 1461215323
DOWNLOAD EBOOKThe 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 Poincar and subsequently developed by Painlev in his famous Leons de Stockholm of 1895. The recent interest in the subject and in the equations investigated by Painlev 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 Cargse 1998, alternate mathematics and physics; they are intended to bring researchers entering the field to the level of present research.
Painleve Equations in the Differential Geometry of Surfaces
Author: Alexander I. Bobenko TU Berlin
Publisher: Springer
Published: 2003-07-01
Total Pages: 125
ISBN-13: 3540444521
DOWNLOAD EBOOKThis book brings together two different branches of mathematics: the theory of Painlev and the theory of surfaces. Self-contained introductions to both these fields are presented. It is shown how some classical problems in surface theory can be solved using the modern theory of Painlev equations. In particular, an essential part of the book is devoted to Bonnet surfaces, i.e. to surfaces possessing families of isometries preserving the mean curvature function. A global classification of Bonnet surfaces is given using both ingredients of the theory of Painlev equations: the theory of isomonodromic deformation and the Painlev property. The book is illustrated by plots of surfaces. It is intended to be used by mathematicians and graduate students interested in differential geometry and Painlev equations. Researchers working in one of these areas can become familiar with another relevant branch of mathematics.
Painlevé Transcendents
Author: Decio Levi
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 454
ISBN-13: 1489911588
DOWNLOAD EBOOKThe 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.
Discrete Differential Geometry
Author: Alexander I. Bobenko TU Berlin
Publisher: Springer Science & Business Media
Published: 2008-03-27
Total Pages: 341
ISBN-13: 3764386215
DOWNLOAD EBOOKThis is the first book on a newly emerging field of discrete differential geometry providing an excellent way to access this exciting area. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. The carefully edited collection of essays gives a lively, multi-facetted introduction to this emerging field.
Isomonodromic Deformations and Frobenius Manifolds
Author: Claude Sabbah
Publisher: Springer Science & Business Media
Published: 2007-12-20
Total Pages: 290
ISBN-13: 1848000545
DOWNLOAD EBOOKBased on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.
Integrable Quantum Field Theories
Author: L. Bonora
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 330
ISBN-13: 1489915168
DOWNLOAD EBOOKProceedings of a NATO ARW held in Como, Italy, September 14-19, 1992
Handbook of Differential Equations: Ordinary Differential Equations
Author: Flaviano Battelli
Publisher: Elsevier
Published: 2008-08-19
Total Pages: 719
ISBN-13: 0080559468
DOWNLOAD EBOOKThis handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. - Covers a variety of problems in ordinary differential equations - Pure mathematical and real-world applications - Written for mathematicians and scientists of many related fields
Isomonodromic Deformations and Applications in Physics
Author: John P. Harnad
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 236
ISBN-13: 0821828045
DOWNLOAD EBOOKThe area of inverse scattering transform method or soliton theory has evolved over the past two decades in a vast variety of exciting new algebraic and analytic directions and has found numerous new applications. Methods and applications range from quantum group theory and exactly solvable statistical models to random matrices, random permutations, and number theory. The theory of isomonodromic deformations of systems of differential equations with rational coefficents, and mostnotably, the related apparatus of the Riemann-Hilbert problem, underlie the analytic side of this striking development. The contributions in this volume are based on lectures given by leading experts at the CRM workshop (Montreal, Canada). Included are both survey articles and more detailed expositionsrelating to the theory of isomonodromic deformations, the Riemann-Hilbert problem, and modern applications. The first part of the book represents the mathematical aspects of isomonodromic deformations; the second part deals mostly with the various appearances of isomonodromic deformations and Riemann-Hilbert methods in the theory of exactly solvable quantum field theory and statistical mechanical models, and related issues. The book elucidates for the first time in the current literature theimportant role that isomonodromic deformations play in the theory of integrable systems and their applications to physics.
