Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Painleve Equations through Symmetry PDF full book. Access full book title Painleve Equations through Symmetry by Masatoshi Noumi. Download full books in PDF and EPUB format.
Author: Masatoshi Noumi Publisher: American Mathematical Soc. ISBN: 0821832212 Category : Mathematics Languages : en Pages : 170
Book Description
This book is devoted to the symmetry of Painleve equations (especially those of types II and IV). The author studies families of transformations for several types of Painleve equationsQthe so-called Backlund transformationsQwhich transform solutions of a given Painleve equation to solutions of the same equation with a different set of parameters. It turns out that these symmetries can be interpreted in terms of root systems associated to affine Weyl groups. The author describes the remarkable combinatorial structures of these symmetries and shows how they are related to the theory of $\tau$-functions associated to integrable systems.
Author: Masatoshi Noumi Publisher: American Mathematical Soc. ISBN: 0821832212 Category : Mathematics Languages : en Pages : 170
Book Description
This book is devoted to the symmetry of Painleve equations (especially those of types II and IV). The author studies families of transformations for several types of Painleve equationsQthe so-called Backlund transformationsQwhich transform solutions of a given Painleve equation to solutions of the same equation with a different set of parameters. It turns out that these symmetries can be interpreted in terms of root systems associated to affine Weyl groups. The author describes the remarkable combinatorial structures of these symmetries and shows how they are related to the theory of $\tau$-functions associated to integrable systems.
Author: Decio Levi Publisher: Springer ISBN: 3319566660 Category : Science Languages : en Pages : 435
Book Description
This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.
Author: Nalini Joshi Publisher: American Mathematical Soc. ISBN: 1470450380 Category : Differential equations, Nonlinear Languages : en Pages : 146
Book Description
Discrete Painlevé 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.
Author: Hans Stephani Publisher: Cambridge University Press ISBN: 9780521366892 Category : Mathematics Languages : en Pages : 278
Book Description
This book provides an introduction to the theory and application of the solution of differential equations using symmetries, a technique of great value in mathematics and the physical sciences. In many branches of physics, mathematics, and engineering, solving a problem means a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The theory and application of such methods have therefore attracted increasing attention in the last two decades. In this text the emphasis is on how to find and use the symmetries in different cases. Many examples are discussed, and the book includes more than 100 exercises. This book will form an introduction accessible to beginning graduate students in physics, applied mathematics, and engineering. Advanced graduate students and researchers in these disciplines will find the book an invaluable reference.
Author: Willi-hans Steeb Publisher: World Scientific Publishing Company ISBN: 9813107014 Category : Science Languages : en Pages : 472
Book Description
This textbook comprehensively introduces students and researchers to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. Covering all the modern techniques in detail, it relates applications to cutting-edge research fields such as Yang-Mills theory and string theory.Aimed at readers in applied mathematics and physics rather than pure mathematics, the material is ideally suited to students and researchers whose main interest lies in finding solutions to differential equations and invariants of maps.A large number of worked examples and challenging exercises help readers to work independently of teachers, and by including SymbolicC++ implementations of the techniques in each chapter, the book takes full advantage of the advancements in algebraic computation.Twelve new sections have been added in this edition, including: Haar measure, Sato's theory and sigma functions, universal algebra, anti-self dual Yang-Mills equation, and discrete Painlevé equations.
Author: Alexander D. Bruno Publisher: Walter de Gruyter ISBN: 311027566X Category : Mathematics Languages : en Pages : 288
Book Description
This is a proceedings of the international conference "Painlevé Equations and Related Topics" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the Steklov Institute of Mathematics of the Russian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011. The survey articles discuss the following topics: General ordinary differential equations Painlevé equations and their generalizations Painlevé property Discrete Painlevé equations Properties of solutions of all mentioned above equations: – Asymptotic forms and asymptotic expansions – Connections of asymptotic forms of a solution near different points – Convergency and asymptotic character of a formal solution – New types of asymptotic forms and asymptotic expansions – Riemann-Hilbert problems – Isomonodromic deformations of linear systems – Symmetries and transformations of solutions – Algebraic solutions Reductions of PDE to Painlevé equations and their generalizations Ordinary Differential Equations systems equivalent to Painlevé equations and their generalizations Applications of the equations and the solutions
Author: Athanassios S. Fokas Publisher: American Mathematical Society ISBN: 1470475561 Category : Mathematics Languages : en Pages : 570
Book Description
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.
Author: A. S. Fokas Publisher: American Mathematical Soc. ISBN: 082183651X Category : Differential equations, Nonlinear Languages : en Pages : 570
Book Description
At the turn of the twentieth century, the French mathematician Paul Painleve 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 Painleve I-VI. Although these equations were initially obtainedanswering 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 Painleve transcendents (i.e., the solutionsof the Painleve 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 Painleve equations are nonlinear, it is still possible, using a new technique called theRiemann-Hilbert formalism, to obtain analogous explicit formulas for the Painleve transcendents. This striking fact, apparently unknown to Painleve and his contemporaries, is the key ingredient for the remarkable applicability of these ``nonlinear special functions''. The book describes in detail theRiemann-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 Painleve functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painleve equations and related areas.
Author: Masatoshi Noumi
Author: Masatoshi Noumi
Author: Masatoshi Noumi
Author: Decio Levi
Author: Nalini Joshi
Author: Hans Stephani
Author: Willi-hans Steeb
Author: Alexander D. Bruno
Author: Athanassios S. Fokas
Author: A. S. Fokas
Author: Peter A. Clarkson