The Isomonodromic Deformation Method In The Theory Of Painlev Equations
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The Isomonodromic Deformation Method In The Theory Of Painlev Equations
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Author : Alexander R. Its
language : en
Publisher: Springer
Release Date : 1986
The Isomonodromic Deformation Method In The Theory Of Painlev Equations written by Alexander R. Its and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
The Isomonodromic Deformation Method In The Theory Of Painleve Equations
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Author : Alexander R. Its
language : en
Publisher:
Release Date : 2014-01-15
The Isomonodromic Deformation Method In The Theory Of Painleve Equations written by Alexander R. Its and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
The Isomonodromic Deformation Method In The Theory Of Painleve Equations
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Author : Alexander R. Its
language : en
Publisher: Springer
Release Date : 2006-11-14
The Isomonodromic Deformation Method In The Theory Of Painleve Equations written by Alexander R. Its and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Painleve Equations In The Differential Geometry Of Surfaces
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Author : Alexander I. Bobenko TU Berlin
language : en
Publisher: Springer
Release Date : 2003-07-01
Painleve Equations In The Differential Geometry Of Surfaces written by Alexander I. Bobenko TU Berlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
This 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.
Painlev Differential Equations In The Complex Plane
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Author : Valerii I. Gromak
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Painlev Differential Equations In The Complex Plane written by Valerii I. Gromak and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
This book is the first comprehensive treatment of Painlevé 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 Painlevé 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, Bäcklund transformations and higher order analogues, treated separately for each of these six equations. The final chapter offers a short overview of applications of Painlevé equations, including an introduction to their discrete counterparts. Due to the present important role of Painlevé 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.
Painlev Transcendents
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Author : Decio Levi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Painlev Transcendents written by Decio Levi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
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.
Pad Methods For Painlev Equations
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Author : Hidehito Nagao
language : en
Publisher: Springer Nature
Release Date : 2021-09-01
Pad Methods For Painlev Equations written by Hidehito Nagao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-01 with Science categories.
The isomonodromic deformation equations such as the Painlevé and Garnier systems are an important class of nonlinear differential equations in mathematics and mathematical physics. For discrete analogs of these equations in particular, much progress has been made in recent decades. Various approaches to such isomonodromic equations are known: the Painlevé test/Painlevé property, reduction of integrable hierarchy, the Lax formulation, algebro-geometric methods, and others. Among them, the Padé method explained in this book provides a simple approach to those equations in both continuous and discrete cases. For a given function f(x), the Padé approximation/interpolation supplies the rational functions P(x), Q(x) as approximants such as f(x)~P(x)/Q(x). The basic idea of the Padé method is to consider the linear differential (or difference) equations satisfied by P(x) and f(x)Q(x). In choosing the suitable approximation problem, the linear differential equations give the Lax pair for some isomonodromic equations. Although this relation between the isomonodromic equations and Padé approximations has been known classically, a systematic study including discrete cases has been conducted only recently. By this simple and easy procedure, one can simultaneously obtain various results such as the nonlinear evolution equation, its Lax pair, and their special solutions. In this way, the method is a convenient means of approaching the isomonodromic deformation equations.
Painlev Transcendents
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Author : Athanassios S. Fokas
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-20
Painlev Transcendents written by Athanassios S. Fokas and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Mathematics categories.
At the turn of the twentieth century, the French mathematician Paul Painlevé and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painlevé I–VI. Although these equations were initially obtained answering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painlevé transcendents (i.e., the solutions of the Painlevé equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points play a crucial role in the applications of these functions. It is shown in this book that even though the six Painlevé equations are nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit formulas for the Painlevé transcendents. This striking fact, apparently unknown to Painlevé and his contemporaries, is the key ingredient for the remarkable applicability of these “nonlinear special functions”. The book describes in detail the Riemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painlevé functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painlevé equations and related areas.
Isomonodromic Deformations And Applications In Physics
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Author : John P. Harnad
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Isomonodromic Deformations And Applications In Physics written by John P. Harnad and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The 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.
Isomonodromic Deformations And Frobenius Manifolds
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Author : Claude Sabbah
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-20
Isomonodromic Deformations And Frobenius Manifolds written by Claude Sabbah and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-20 with Mathematics categories.
Based 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.