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Painleve Analysis And Its Applications
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Book Synopsis Painleve Analysis and Its Applications by : Amit K. Roy-Chowdhury
Download or read book Painleve Analysis and Its Applications written by Amit K. Roy-Chowdhury and published by CRC Press. This book was released on 1999-12-27 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: With interest in the study of nonlinear systems at an all-time high, researchers are eager to explore the mysteries behind the nonlinear equations that govern various physical processes. Painléve analysis may be the only tool available that allows the analysis of both integrable and non-integrable systems. With a primary objective of introducing the uninitiated to the various techniques of the Painlevé approach, this monograph brings together the results of the extensive research performed in the field over the last few decades. For the first time in a single volume, this book offers treatment of both the theory of Painlevé analysis and its practical applications. In it, the author addresses the soliton and nonlinearity, Painlevé analysis and the integrability of ordinary and partial differential equations, Painlevé properties, different forms of expansion, and the relation of Painlevé expansion with conformal invariance. He also gives a detailed account of negative resonances, explains the connection with monodromy, and demonstrates applications to specific important equations. Painlevé Analysis and Its Applications offers a clear presentation and down-to-earth approach that includes many examples and requires only a basic understanding of complex function theory and differential equations.
Book Synopsis Painleve Analysis and Its Applications by : A.R. Chowdhury
Download or read book Painleve Analysis and Its Applications written by A.R. Chowdhury and published by . This book was released on 1999-05-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Painlevé Transcendents by : Decio Levi
Download or read book Painlevé Transcendents written by Decio Levi and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Painlevé Handbook by : Robert Conte
Download or read book The Painlevé Handbook written by Robert Conte and published by Springer Nature. This book was released on 2020-11-07 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances in Nonlinear Partial Differential Equations and Related Areas by : Gui-Qiang Chen
Download or read book Advances in Nonlinear Partial Differential Equations and Related Areas written by Gui-Qiang Chen and published by World Scientific. This book was released on 1998 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of research papers on nonlinear partial differential equations and related areas, representing many aspects of the most recent developments in these important areas. In particular, the following are included: nonlinear conservation laws, semilinear elliptic equations, nonlinear hyperbolic equations, nonlinear parabolic equations, singular limit problems, and analysis of exact and numerical solutions. Important areas such as numerical analysis, relaxation theory, multiphase theory, kinetic theory, combustion theory, dynamical systems, and quantum field theory are also covered.
Book Synopsis Nonlinear Evolution Equations And Painleve Test by : N Euler
Download or read book Nonlinear Evolution Equations And Painleve Test written by N Euler and published by World Scientific. This book was released on 1988-10-01 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an edited version of lectures given by the authors at a seminar at the Rand Afrikaans University. It gives a survey on the Painlevé test, Painlevé property and integrability. Both ordinary differential equations and partial differential equations are considered.
Book Synopsis Painlevé Differential Equations in the Complex Plane by : Valerii I. Gromak
Download or read book Painlevé Differential Equations in the Complex Plane written by Valerii I. Gromak and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computer Algebra and Geometric Algebra with Applications by : Hongbo Li
Download or read book Computer Algebra and Geometric Algebra with Applications written by Hongbo Li and published by Springer. This book was released on 2005-06-20 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: MathematicsMechanization consistsoftheory,softwareandapplicationofc- puterized mathematical activities such as computing, reasoning and discovering. ItsuniquefeaturecanbesuccinctlydescribedasAAA(Algebraization,Algori- mization, Application). The name “Mathematics Mechanization” has its origin in the work of Hao Wang (1960s), one of the pioneers in using computers to do research in mathematics, particularly in automated theorem proving. Since the 1970s, this research direction has been actively pursued and extensively dev- oped by Prof. Wen-tsun Wu and his followers. It di?ers from the closely related disciplines like Computer Mathematics, Symbolic Computation and Automated Reasoning in that its goal is to make algorithmic studies and applications of mathematics the major trend of mathematics development in the information age. The International Workshop on Mathematics Mechanization (IWMM) was initiated by Prof. Wu in 1992, and has ever since been held by the Key L- oratory of Mathematics Mechanization (KLMM) of the Chinese Academy of Sciences. There have been seven workshops of the series up to now. At each workshop, several experts are invited to deliver plenary lectures on cutting-edge methods and algorithms of the selected theme. The workshop is also a forum for people working on related subjects to meet, collaborate and exchange ideas.
Book Synopsis Painlevé Transcendents by : Athanassios S. Fokas
Download or read book Painlevé Transcendents written by Athanassios S. Fokas and published by American Mathematical Society. This book was released on 2023-11-20 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances In Nonlinear Partial Differential Equations And Related Areas: A Volume In Honor Of Prof Xia by : Gui-qiang Chen
Download or read book Advances In Nonlinear Partial Differential Equations And Related Areas: A Volume In Honor Of Prof Xia written by Gui-qiang Chen and published by World Scientific. This book was released on 1998-12-04 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of research papers on nonlinear partial differential equations and related areas, representing many aspects of the most recent developments in these important areas. In particular, the following are included: nonlinear conservation laws, semilinear elliptic equations, nonlinear hyperbolic equations, nonlinear parabolic equations, singular limit problems, and analysis of exact and numerical solutions. Important areas such as numerical analysis, relaxation theory, multiphase theory, kinetic theory, combustion theory, dynamical systems, and quantum field theory are also covered.
Book Synopsis Painleve Transcendents by : A. S. Fokas
Download or read book Painleve Transcendents written by A. S. Fokas and published by American Mathematical Soc.. This book was released on 2006 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Integrability, Painlevé Geometry and Lie Algebras by : Mark Adler
Download or read book Algebraic Integrability, Painlevé Geometry and Lie Algebras written by Mark Adler and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.
Book Synopsis The Painlevé Property by : Robert Conte
Download or read book The Painlevé Property written by Robert Conte and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Partition Functions and Automorphic Forms by : Valery A. Gritsenko
Download or read book Partition Functions and Automorphic Forms written by Valery A. Gritsenko and published by Springer Nature. This book was released on 2020-07-09 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.
Book Synopsis Handbook of Nonlinear Partial Differential Equations by : Andrei D. Polyanin
Download or read book Handbook of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2004-06-02 with total page 835 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Book Synopsis Handbook of Ordinary Differential Equations by : Andrei D. Polyanin
Download or read book Handbook of Ordinary Differential Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2017-11-15 with total page 1584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.
Book Synopsis Theory and Applications of Special Functions by : Mourad E. H. Ismail
Download or read book Theory and Applications of Special Functions written by Mourad E. H. Ismail and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles on various aspects of q-series and special functions dedicated to Mizan Rahman. It also includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject.
