Painleve Transcendents

Painleve Transcendents Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Painleve Transcendents book. This book definitely worth reading, it is an incredibly well-written.

Painlevé Transcendents

Decio Levi,Pavel Winternitz
Painlev Transcendents Book PDF

Author : Decio Levi,Pavel Winternitz
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 44,9 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781489911582

Get Book

Painlevé Transcendents by Decio Levi,Pavel Winternitz Pdf

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.

Painlevé Transcendents

Athanassios S. Fokas,Alexander R. Its,Andrei A. Kapaev,Victor Yu. Novokshenov
Painlev Transcendents Book PDF

Author : Athanassios S. Fokas,Alexander R. Its,Andrei A. Kapaev,Victor Yu. Novokshenov
Publisher : American Mathematical Society
Page : 570 pages
File Size : 49,7 Mb
Release : 2023-11-20
Category : Mathematics
ISBN : 9781470475567

Get Book

Painlevé Transcendents by Athanassios S. Fokas,Alexander R. Its,Andrei A. Kapaev,Victor Yu. Novokshenov Pdf

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.

Painlevé Differential Equations in the Complex Plane

Valerii I. Gromak,Ilpo Laine,Shun Shimomura
Painlev Differential Equations in the Complex Plane Book PDF

Author : Valerii I. Gromak,Ilpo Laine,Shun Shimomura
Publisher : Walter de Gruyter
Page : 313 pages
File Size : 54,6 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110198096

Get Book

Painlevé Differential Equations in the Complex Plane by Valerii I. Gromak,Ilpo Laine,Shun Shimomura Pdf

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.

The Painlevé Handbook

Robert Conte,Micheline Musette
The Painlev Handbook Book PDF

Author : Robert Conte,Micheline Musette
Publisher : Springer Nature
Page : 389 pages
File Size : 43,9 Mb
Release : 2020-11-07
Category : Science
ISBN : 9783030533403

Get Book

The Painlevé Handbook by Robert Conte,Micheline Musette Pdf

This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlevé test and shows how Painlevé analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schrödinger equation, the Korteweg-de Vries equation, Hénon-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic and quintic Ginzburg-Landau equations. Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic Ginzburg-Landau equations; a close look at physical problems involving the sixth Painlevé function; and an overview of new results since the book’s original publication with special focus on finite difference equations. The book features tutorials, appendices, and comprehensive references, and will appeal to graduate students and researchers in both mathematics and the physical sciences.

Orthogonal Polynomials and Special Functions

Francisco Marcellàn,Walter Van Assche
Orthogonal Polynomials and Special Functions Book PDF

Author : Francisco Marcellàn,Walter Van Assche
Publisher : Springer
Page : 422 pages
File Size : 40,9 Mb
Release : 2006-10-18
Category : Mathematics
ISBN : 9783540367161

Get Book

Orthogonal Polynomials and Special Functions by Francisco Marcellàn,Walter Van Assche Pdf

Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? The present set of lecture notes contains seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions.

Handbook of Nonlinear Partial Differential Equations, Second Edition

Andrei D. Polyanin,Valentin F. Zaitsev
Handbook of Nonlinear Partial Differential Equations Second Edition Book PDF

Author : Andrei D. Polyanin,Valentin F. Zaitsev
Publisher : CRC Press
Page : 1878 pages
File Size : 45,9 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781420087246

Get Book

Handbook of Nonlinear Partial Differential Equations, Second Edition by Andrei D. Polyanin,Valentin F. Zaitsev Pdf

New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.

Painleve Equations in the Differential Geometry of Surfaces

Alexander I. Bobenko TU Berlin,Ulrich Eitner
Painleve Equations in the Differential Geometry of Surfaces Book PDF

Author : Alexander I. Bobenko TU Berlin,Ulrich Eitner
Publisher : Springer
Page : 120 pages
File Size : 43,9 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540444527

Get Book

Painleve Equations in the Differential Geometry of Surfaces by Alexander I. Bobenko TU Berlin,Ulrich Eitner Pdf

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.

The Kowalevski Property

Vadim B. Kuznetsov
The Kowalevski Property Book PDF

Author : Vadim B. Kuznetsov
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 48,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 082187330X

Get Book

The Kowalevski Property by Vadim B. Kuznetsov Pdf

This book is a collection of survey articles on several topics related to the general notion of integrability. It stems from a workshop on ''Mathematical Methods of Regular Dynamics'' dedicated to Sophie Kowalevski. Leading experts introduce corresponding areas in depth. The book provides a broad overview of research, from the pioneering work of the nineteenth century to the developments of the 1970s through the present. The book begins with two historical papers by R. L. Cooke onKowalevski's life and work. Following are 15 research surveys on integrability issues in differential and algebraic geometry, classical complex analysis, discrete mathematics, spinning tops, Painleve equations, global analysis on manifolds, special functions, etc. It concludes with Kowalevski's famouspaper published in Acta Mathematica in 1889, ''Sur le probleme de la rotation d'un corps solide autour d'un point fixe''. The book is suitable for graduate students in pure and applied mathematics, the general mathematical audience studying integrability, and research mathematicians interested in differential and algebraic geometry, analysis, and special functions.

The Painlevé Property

Robert Conte
The Painlev Property Book PDF

Author : Robert Conte
Publisher : Springer Science & Business Media
Page : 828 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461215325

Get Book

The Painlevé Property by Robert Conte Pdf

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 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.

Special Functions and Orthogonal Polynomials

AMS Special Session on Special Functions and Orthogonal Polynomials
Special Functions and Orthogonal Polynomials Book PDF

Author : AMS Special Session on Special Functions and Orthogonal Polynomials
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 49,9 Mb
Release : 2008
Category : Functions, Special
ISBN : 9780821846506

Get Book

Special Functions and Orthogonal Polynomials by AMS Special Session on Special Functions and Orthogonal Polynomials Pdf

"This volume contains fourteen articles that represent the AMS Special Session on Special Functions and Orthogonal Polynomials, held in Tucson, Arizona in April of 2007. It gives an overview of the modern field of special functions with all major subfields represented, including: applications to algebraic geometry, asymptotic analysis, conformal mapping, differential equations, elliptic functions, fractional calculus, hypergeometric and q-hypergeometric series, nonlinear waves, number theory, symbolic and numerical evaluation of integrals, and theta functions. A few articles are expository, with extensive bibliographies, but all contain original research." "This book is intended for pure and applied mathematicians who are interested in recent developments in the theory of special functions. It covers a wide range of active areas of research and demonstrates the vitality of the field."--BOOK JACKET.

Algebraic Analysis of Differential Equations

T. Aoki,H. Majima,Y. Takei,N. Tose
Algebraic Analysis of Differential Equations Book PDF

Author : T. Aoki,H. Majima,Y. Takei,N. Tose
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 54,9 Mb
Release : 2009-03-15
Category : Mathematics
ISBN : 9784431732402

Get Book

Algebraic Analysis of Differential Equations by T. Aoki,H. Majima,Y. Takei,N. Tose Pdf

This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.

Invertible Point Transformations and Nonlinear Differential Equations

Willi-Hans Steeb
Invertible Point Transformations and Nonlinear Differential Equations Book PDF

Author : Willi-Hans Steeb
Publisher : World Scientific
Page : 188 pages
File Size : 51,7 Mb
Release : 1993-06-04
Category : Science
ISBN : 9789814504362

Get Book

Invertible Point Transformations and Nonlinear Differential Equations by Willi-Hans Steeb Pdf

The invertible point transformation is a powerful tool in the study of nonlinear differential and difference equations. This book gives a comprehensive introduction to this technique. Ordinary and partial differential equations are studied with this approach. The book also covers nonlinear difference equations. The connections with Lie symmetries, the Painlevé property, first integrals and the Cartan equivalence method are discussed in detail. Most of the evaluations are checked with the computer language REDUCE; the book includes 30 REDUCE programs. A short introduction to the jet bundle formalism is given. Contents:First-Order Ordinary Differential EquationSecond-Order Ordinary Differential EquationsThird-Order Differential EquationsLie Point SymmetriesFirst Integrals and Differential EquationCartan Equivalence MethodPainlevé Test and LinearizationPainlevé Test and Partial Differential EquationsPartial Differential EquationsDifference EquationsREDUCE ProgramsJet Bundle Formalism Readership: Mathematicians, physicists and engineers. keywords:Nonlinear Differential Equations;Invertible Point Transformation;Lie Point Symmetries;Painleve Test;Jet Bundle Formalism “The text is well written, and fairly elementary from a mathematical standpoint. The concepts are clearly illustrated; there are numerous examples of interest to applied mathematicians and physicists.” SIAM Review

Bifurcation Phenomena in Mathematical Physics and Related Topics

C. Bardos,D. Bessis
Bifurcation Phenomena in Mathematical Physics and Related Topics Book PDF

Author : C. Bardos,D. Bessis
Publisher : Springer Science & Business Media
Page : 591 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400990043

Get Book

Bifurcation Phenomena in Mathematical Physics and Related Topics by C. Bardos,D. Bessis Pdf

One of the main ideas in organizing the Summer Institute of Cargese on "Bifurcation Phenomena in Mathematical Physics and Related Topics" was to bring together Physicists and Mathematicians working on the properties arising from the non linearity of the phenomena and of the models that are used for their description. Among these properties the existence of bifurcations is one of the most interesting, and we had a general survey of the mathematical tools used in this field. This survey was done by M. Crandall and P. Rabinowitz and the notes enclosed in these proceedings were written by E. Buzano a]ld C. Canuto. Another mathematical approach, using Morse Theory was given by J. Smoller reporting on a joint work with C. Conley. An example of a direct application was given by M. Ghil. For physicists the theory of bifurcation is closely related to critical phenomena and this was explained in a series of talks given by J.P. Eckmann, G. Baker and M. Fisher. Some related ideas can be found in the talk given by T. T. Wu , on a joint work with Barry Mc Coy on quantum field theory. The description of these phenomena leads to the use of Pade approximants (it is explained for instance in the lectures of J. Nuttall) and then to some problems in drop hot moment problems. (cf. the lecture of D. Bessis).

String-Math 2016

Amir-Kian Kashani-Poor,Ruben Minasian,Nikita Nekrasov,Boris Pioline
String Math 2016 Book PDF

Author : Amir-Kian Kashani-Poor,Ruben Minasian,Nikita Nekrasov,Boris Pioline
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 50,6 Mb
Release : 2018-06-06
Category : Geometry, Algebraic
ISBN : 9781470435158

Get Book

String-Math 2016 by Amir-Kian Kashani-Poor,Ruben Minasian,Nikita Nekrasov,Boris Pioline Pdf

This volume contains the proceedings of the conference String-Math 2016, which was held from June 27–July 2, 2016, at Collége de France, Paris, France. String-Math is an annual conference covering the most significant progress at the interface of string theory and mathematics. The two fields have had a very fruitful dialogue over the last thirty years, with string theory contributing key ideas which have opened entirely new areas of mathematics and modern mathematics providing powerful concepts and tools to deal with the intricacies of string and quantum field theory. The papers in this volume cover topics ranging from supersymmetric quantum field theories, topological strings, and conformal nets to moduli spaces of curves, representations, instantons, and harmonic maps, with applications to spectral theory and to the geometric Langlands program.

Théories Asymptotiques Et Équations de Painlevé

Éric Delabaere,Michèle Loday-Richaud
Th ories Asymptotiques Et quations de Painlev Book PDF

Author : Éric Delabaere,Michèle Loday-Richaud
Publisher : Soci't' Math'matique de France
Page : 398 pages
File Size : 47,7 Mb
Release : 2006
Category : Differential equations
ISBN : UVA:X030255673

Get Book

Théories Asymptotiques Et Équations de Painlevé by Éric Delabaere,Michèle Loday-Richaud Pdf

The major part of this volume is devoted to the study of the sixth Painleve equation through a variety of approaches, namely elliptic representation, the classification of algebraic solutions and so-called ``dessins d'enfants'' deformations, affine Weyl group symmetries and dynamics using the techniques of Riemann-Hilbert theory and those of algebraic geometry. Discrete Painleve equations and higher order equations, including the mKdV hierarchy and its Lax pair and a WKB analysis of perturbed Noumi-Yamada systems, are given a place of study, as well as theoretical settings in Galois theory for linear and non-linear differential equations, difference and $q$-difference equations with applications to Painleve equations and to integrability or non-integrability of certain Hamiltonian systems.